To add a saved search as a custom sublist in the custom record. follow the below steps.
Step 1: create a saved search then check AVAILABLE AS SUBLIST VIEW in the saved search then go to the available filters tab and add at least one available filter(the filter field type should be List/Record).
Step 2: go to your custom record then click on the sublists tab then add your saved search from the search line dropdown.
Note: On the Available Filters subtab, the first filter listed must be of type List/Record for this saved search to be available as a custom sublist