Hi @Anonymous, you can filter the dropdown by the current user with the following statement:
Filter(ListName, User().Email in PersonField.Email)
Should the User.Email() not match the mail within the Person field, you could also add the Office365 Users connector and replace User().Email:
Filter(ListName, Office365Users.MyProfileV2().mail in PersonField.Email)
However, the 'in' will make your filter not delegable. Should you have a long list (>500 or >2000 dependent on app settings) or this list will slowly grow to those numbers, I would suggest looking for delegable alternatives.
I recently came across a great article written by @WarrenBelz,. The article mainly tackles multi select combobox filtering but It might also be applicable to this case.
I hope this helps!