There are two options to limit the records displayed in the Record Finder:
Set a Records Filter on the field.
Only show records linked to the logged-in user in the finder (Record Finder section).
To use the second option, the login feature must be turned ON and the table where the linked records field is located must be linked to the user table. This toggle would only show up for linked records fields in the child form, not the parent form.
As an illustration, suppose Table 1 represents a user table, and it has a linked records field connected to Table 2. In Table 2, there is another linked records field that connects to Table 3. Suppose you want to implement the second option for Table 3. In that case, Table 1 and Table 3 must have a direct connection to each other.