Assigning test suite execution records while executing the failed testcases

Do you want to run the failed test cases or failed test suite. If you run the failed test suite, all the test cases within it will be executed. You can also run the failed test cases independently. In that case, it will not be associated with any test suite

There is no direct connection between running  a TSER and running a TCER.
A TSER execution should be looked from suite execution perspective. Either whole suite pass or fails. It should be more of what is the goal of the suite rather what individual steps in the suite.
If one of the testcase failed in suite execution, you can either rerun the whole suite to make sure everything pass or can just run only those testcases which failed in last run.
When you run a individual TCER, it is in the context of goal for the Testcase. It has no relation with Test suite even same test case is also part one or more Test Suite.

"REPLY, not ANSWER": The question was "how", the above answer does not indicate "how" you execute just the failed test cases within the suite.