You can filter the linked records using the options found in the Filter Records section of your field's settings.
The filter can be applied to linked records in 2 locations:
1. Record Finder
By default, the filters apply to the list of records shown in the linked records selector (which you might have chosen to hide on your form).
Personal Records
There's also an option to limit the selectable records to only records that are linked to the logged-in user and hide the ones that are not connected to the logged-in user. You'll find it under "Choose Records to Display".
This feature is only available if:
The login feature is turned ON, and
The table of the linked records field contains a linked field to the users table.
*This toggle would only show up for linked records fields in the child form, not the parent form. This will only affect the records that are showing up in the Record Finder, not the existing values.
Example
If 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 apply the filter to Table 3. In that case, Table 1 and Table 3 must have a direct connection to each other.
2. Selected Records
When the Filter application mode is set to Record Finder + Selected records, the filter will also apply to the records that already exist in the cell. They will be hidden if they do not pass conditions. However, it doesn't apply to newly created records on the form via Create New.