Does querying int column with string datatype have any performance impact in mysql queries?

It should be fine to do this either way for an indexed integer column. When you compare an integer column to a constant, the constant value is cast to an integer whether you format it as an integer or a string.

You can confirm this with EXPLAIN. In both cases, the EXPLAIN shows that it will use the index (type: ref indicates an index lookup), and the performance will be the same.

mysql> explain select * from any_table where any_column_1 = 12345;
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+
| id | select_type | table     | partitions | type | possible_keys              | key                        | key_len | ref   | rows | filtered | Extra |
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+
|  1 | SIMPLE      | any_table | NULL       | ref  | any_table_any_column_1_IDX | any_table_any_column_1_IDX | 5       | const |    1 |   100.00 | NULL  |
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+

mysql> explain select * from any_table where any_column_1 = '12345';
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+
| id | select_type | table     | partitions | type | possible_keys              | key                        | key_len | ref   | rows | filtered | Extra |
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+
|  1 | SIMPLE      | any_table | NULL       | ref  | any_table_any_column_1_IDX | any_table_any_column_1_IDX | 5       | const |    1 |   100.00 | NULL  |
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+

If you had indexed the string column in your example, any_column_2, it would make a difference because the collation of a string column must match the collation of the value you compare it to. A string literal will be cast to a compatible collation by default, so it uses the index:

create index any_table_any_column_2_IDX USING BTREE ON any_table (any_column_2);

mysql> explain select * from any_table where any_column_2 = '12345';
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+
| id | select_type | table     | partitions | type | possible_keys              | key                        | key_len | ref   | rows | filtered | Extra |
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+
|  1 | SIMPLE      | any_table | NULL       | ref  | any_table_any_column_2_IDX | any_table_any_column_2_IDX | 768     | const |    1 |   100.00 | NULL  |
+----+-------------+-----------+------------+------+----------------------------+----------------------------+---------+-------+------+----------+-------+

But an integer literal has no collation, so you get warnings, and the index cannot be used. The EXPLAIN shows type: ALL so it will do a table-scan and that will have poor performance if you query a table with many rows.

mysql> explain select * from any_table where any_column_2 = 12345;
+----+-------------+-----------+------------+------+----------------------------+------+---------+------+------+----------+-------------+
| id | select_type | table     | partitions | type | possible_keys              | key  | key_len | ref  | rows | filtered | Extra       |
+----+-------------+-----------+------------+------+----------------------------+------+---------+------+------+----------+-------------+
|  1 | SIMPLE      | any_table | NULL       | ALL  | any_table_any_column_2_IDX | NULL | NULL    | NULL |    1 |   100.00 | Using where |
+----+-------------+-----------+------------+------+----------------------------+------+---------+------+------+----------+-------------+
1 row in set, 3 warnings (0.00 sec)

mysql> show warnings;
+---------+------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Level   | Code | Message                                                                                                                                                                                                     |
+---------+------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Warning | 1739 | Cannot use ref access on index 'any_table_any_column_2_IDX' due to type or collation conversion on field 'any_column_2'                                                                                     |
| Warning | 1739 | Cannot use range access on index 'any_table_any_column_2_IDX' due to type or collation conversion on field 'any_column_2'                                                                                   |
| Note    | 1003 | /* select#1 */ select `test2`.`any_table`.`any_column_1` AS `any_column_1`,`test2`.`any_table`.`any_column_2` AS `any_column_2` from `test2`.`any_table` where (`test2`.`any_table`.`any_column_2` = 12345) |
+---------+------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+