We can say 六月十六號是父親節 ( June 16th is Father's Day ).
We often call our elderly daddy 老爹 (Old Dad). Similar to Mandarin.
We should also say " 老竇我好掛住你啊 ！” ( = Daddy, how I miss you! ) if you call home from far away. Take good care of your father and send him more love if you still can. I cannot any more as he passed away many years ago. There's a Chinese saying from a famous peom: 子欲養而親不待 ( When the son wants to support the parents who have passed away. ) A pretty close translation of the sentences in that Chinese poem can be found at Dict.cn: 树欲静而风不止，子欲养而亲不待.