diff --git a/cmd/explaintest/r/explain_easy.result b/cmd/explaintest/r/explain_easy.result
index 214e51b366de1..c2c61bf79b58e 100644
--- a/cmd/explaintest/r/explain_easy.result
+++ b/cmd/explaintest/r/explain_easy.result
@@ -124,11 +124,12 @@ Projection	10000.00	root		eq(test.t1.c2, test.t2.c2)->Column#11
 └─Apply	10000.00	root		CARTESIAN left outer join
   ├─TableReader(Build)	10000.00	root		data:TableFullScan
   │ └─TableFullScan	10000.00	cop[tikv]	table:t1	keep order:false, stats:pseudo
-  └─Projection(Probe)	1.00	root		test.t2.c1, test.t2.c2
-    └─IndexLookUp	1.00	root		limit embedded(offset:0, count:1)
-      ├─Limit(Build)	1.00	cop[tikv]		offset:0, count:1
-      │ └─IndexRangeScan	1.00	cop[tikv]	table:t2, index:c1(c1)	range: decided by [eq(test.t1.c1, test.t2.c1)], keep order:true, stats:pseudo
-      └─TableRowIDScan(Probe)	1.00	cop[tikv]	table:t2	keep order:false, stats:pseudo
+  └─Limit(Probe)	1.00	root		offset:0, count:1
+    └─Projection	1.00	root		test.t2.c1, test.t2.c2
+      └─IndexLookUp	1.00	root		
+        ├─Limit(Build)	1.00	cop[tikv]		offset:0, count:1
+        │ └─IndexRangeScan	1.00	cop[tikv]	table:t2, index:c1(c1)	range: decided by [eq(test.t1.c1, test.t2.c1)], keep order:true, stats:pseudo
+        └─TableRowIDScan(Probe)	1.00	cop[tikv]	table:t2	keep order:false, stats:pseudo
 explain format = 'brief' select * from t1 order by c1 desc limit 1;
 id	estRows	task	access object	operator info
 Limit	1.00	root		offset:0, count:1
diff --git a/cmd/explaintest/r/explain_easy_stats.result b/cmd/explaintest/r/explain_easy_stats.result
index e76b0d4d233a6..8305dfa929e2b 100644
--- a/cmd/explaintest/r/explain_easy_stats.result
+++ b/cmd/explaintest/r/explain_easy_stats.result
@@ -106,11 +106,12 @@ Projection	1999.00	root		eq(test.t1.c2, test.t2.c2)->Column#11
 └─Apply	1999.00	root		CARTESIAN left outer join
   ├─TableReader(Build)	1999.00	root		data:TableFullScan
   │ └─TableFullScan	1999.00	cop[tikv]	table:t1	keep order:false
-  └─Projection(Probe)	1.00	root		test.t2.c1, test.t2.c2
-    └─IndexLookUp	1.00	root		limit embedded(offset:0, count:1)
-      ├─Limit(Build)	1.00	cop[tikv]		offset:0, count:1
-      │ └─IndexRangeScan	1.25	cop[tikv]	table:t2, index:c1(c1)	range: decided by [eq(test.t1.c1, test.t2.c1)], keep order:true
-      └─TableRowIDScan(Probe)	1.00	cop[tikv]	table:t2	keep order:false, stats:pseudo
+  └─Limit(Probe)	1.00	root		offset:0, count:1
+    └─Projection	1.00	root		test.t2.c1, test.t2.c2
+      └─IndexLookUp	1.00	root		
+        ├─Limit(Build)	1.00	cop[tikv]		offset:0, count:1
+        │ └─IndexRangeScan	1.25	cop[tikv]	table:t2, index:c1(c1)	range: decided by [eq(test.t1.c1, test.t2.c1)], keep order:true
+        └─TableRowIDScan(Probe)	1.00	cop[tikv]	table:t2	keep order:false, stats:pseudo
 explain format = 'brief' select * from t1 order by c1 desc limit 1;
 id	estRows	task	access object	operator info
 Limit	1.00	root		offset:0, count:1
diff --git a/executor/partition_table_test.go b/executor/partition_table_test.go
index 34066a301bff4..84bf7513a6514 100644
--- a/executor/partition_table_test.go
+++ b/executor/partition_table_test.go
@@ -2403,6 +2403,42 @@ func (s *partitionTableSuite) TestDirectReadingWithAgg(c *C) {
 	}
 }
 
+func (s *partitionTableSuite) TestIssue24636(c *C) {
+	tk := testkit.NewTestKitWithInit(c, s.store)
+	tk.MustExec("create database test_issue_24636")
+	tk.MustExec("use test_issue_24636")
+
+	tk.MustExec(`CREATE TABLE t (a int, b date, c int, PRIMARY KEY (a,b))
+		PARTITION BY RANGE ( TO_DAYS(b) ) (
+		  PARTITION p0 VALUES LESS THAN (737821),
+		  PARTITION p1 VALUES LESS THAN (738289)
+		)`)
+	tk.MustExec(`INSERT INTO t (a, b, c) VALUES(0, '2021-05-05', 0)`)
+	tk.MustQuery(`select c from t use index(primary) where a=0 limit 1`).Check(testkit.Rows("0"))
+
+	tk.MustExec(`
+		CREATE TABLE test_partition (
+		  a varchar(100) NOT NULL,
+		  b date NOT NULL,
+		  c varchar(100) NOT NULL,
+		  d datetime DEFAULT NULL,
+		  e datetime DEFAULT NULL,
+		  f bigint(20) DEFAULT NULL,
+		  g bigint(20) DEFAULT NULL,
+		  h bigint(20) DEFAULT NULL,
+		  i bigint(20) DEFAULT NULL,
+		  j bigint(20) DEFAULT NULL,
+		  k bigint(20) DEFAULT NULL,
+		  l bigint(20) DEFAULT NULL,
+		  PRIMARY KEY (a,b,c) /*T![clustered_index] NONCLUSTERED */
+		) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin
+		PARTITION BY RANGE ( TO_DAYS(b) ) (
+		  PARTITION pmin VALUES LESS THAN (737821),
+		  PARTITION p20200601 VALUES LESS THAN (738289))`)
+	tk.MustExec(`INSERT INTO test_partition (a, b, c, d, e, f, g, h, i, j, k, l) VALUES('aaa', '2021-05-05', '428ff6a1-bb37-42ac-9883-33d7a29961e6', '2021-05-06 08:13:38', '2021-05-06 13:28:08', 0, 8, 3, 0, 9, 1, 0)`)
+	tk.MustQuery(`select c,j,l from test_partition where c='428ff6a1-bb37-42ac-9883-33d7a29961e6' and a='aaa' limit 0, 200`).Check(testkit.Rows("428ff6a1-bb37-42ac-9883-33d7a29961e6 9 0"))
+}
+
 func (s *partitionTableSuite) TestIdexMerge(c *C) {
 	if israce.RaceEnabled {
 		c.Skip("exhaustive types test, skip race test")
diff --git a/planner/core/exhaust_physical_plans.go b/planner/core/exhaust_physical_plans.go
index a0c0072e94a33..0d8b183a6900a 100644
--- a/planner/core/exhaust_physical_plans.go
+++ b/planner/core/exhaust_physical_plans.go
@@ -2061,6 +2061,7 @@ func (lt *LogicalTopN) getPhysLimits(prop *property.PhysicalProperty) []Physical
 			Count:  lt.Count,
 			Offset: lt.Offset,
 		}.Init(lt.ctx, lt.stats, lt.blockOffset, resultProp)
+		limit.SetSchema(lt.Schema())
 		ret = append(ret, limit)
 	}
 	return ret
diff --git a/planner/core/task.go b/planner/core/task.go
index d3b8b84d78ead..c1b925451ca1b 100644
--- a/planner/core/task.go
+++ b/planner/core/task.go
@@ -1127,6 +1127,16 @@ func (p *PhysicalLimit) sinkIntoIndexLookUp(t task) bool {
 			return false
 		}
 	}
+
+	// If this happens, some Projection Operator must be inlined into this Limit. (issues/14428)
+	// For example, if the original plan is `IndexLookUp(col1, col2) -> Limit(col1, col2) -> Project(col1)`,
+	//  then after inlining the Project, it will be `IndexLookUp(col1, col2) -> Limit(col1)` here.
+	// If the Limit is sunk into the IndexLookUp, the IndexLookUp's schema needs to be updated as well,
+	//  but updating it here is not safe, so do not sink Limit into this IndexLookUp in this case now.
+	if p.Schema().Len() != reader.Schema().Len() {
+		return false
+	}
+
 	// We can sink Limit into IndexLookUpReader only if tablePlan contains no Selection.
 	ts, isTableScan := reader.tablePlan.(*PhysicalTableScan)
 	if !isTableScan {
diff --git a/planner/core/testdata/integration_suite_out.json b/planner/core/testdata/integration_suite_out.json
index 77aa5b1494da7..72d5c968d7468 100644
--- a/planner/core/testdata/integration_suite_out.json
+++ b/planner/core/testdata/integration_suite_out.json
@@ -14,11 +14,12 @@
       {
         "SQL": "explain format = 'brief' select * from tbl use index(idx_b_c) where b > 1 order by b desc limit 2,1",
         "Plan": [
-          "Projection 1.00 root  test.tbl.a, test.tbl.b, test.tbl.c",
-          "└─IndexLookUp 1.00 root  limit embedded(offset:2, count:1)",
-          "  ├─Limit(Build) 3.00 cop[tikv]  offset:0, count:3",
-          "  │ └─IndexRangeScan 3.00 cop[tikv] table:tbl, index:idx_b_c(b, c) range:(1,+inf], keep order:true, desc",
-          "  └─TableRowIDScan(Probe) 1.00 cop[tikv] table:tbl keep order:false, stats:pseudo"
+          "Limit 1.00 root  offset:2, count:1",
+          "└─Projection 3.00 root  test.tbl.a, test.tbl.b, test.tbl.c",
+          "  └─IndexLookUp 3.00 root  ",
+          "    ├─Limit(Build) 3.00 cop[tikv]  offset:0, count:3",
+          "    │ └─IndexRangeScan 3.00 cop[tikv] table:tbl, index:idx_b_c(b, c) range:(1,+inf], keep order:true, desc",
+          "    └─TableRowIDScan(Probe) 3.00 cop[tikv] table:tbl keep order:false, stats:pseudo"
         ]
       },
       {