It’s a sentence fragment, so it can’t be assessed for case. The full sentence could be “this is my dad and me” or “my dad and I have this tradition”.
Besides, it’s long been shown that with two or more pronouns in coordination (ie connecting pronouns with “and”), natives often use a different pronoun than they would with just a single one. It’s probably still not widely acceptable in formal contexts, but in informal text many people wouldn’t bat an eye. It may even be more acceptable in certain dialects than the formal prescribed grammar.
It’s a sentence fragment, so it can’t be assessed for case. The full sentence could be “this is my dad and me” or “my dad and I have this tradition”.
Besides, it’s long been shown that with two or more pronouns in coordination (ie connecting pronouns with “and”), natives often use a different pronoun than they would with just a single one. It’s probably still not widely acceptable in formal contexts, but in informal text many people wouldn’t bat an eye. It may even be more acceptable in certain dialects than the formal prescribed grammar.