Is it permissible to supplicate to be reunited with one's deceased father and to see him with the Prophet Muhammad (peace be upon him) at the gate of Paradise, to drink from his Fount, and to enter Paradise together? And is there a specific supplication for that?

Praying for mercy for one's parents and for reunion with them in Paradise or in the Barzakh is permissible. However, praying to see them with the Prophet at the gate of Paradise and beyond involves an objectionable exaggeration, due to the Prophet's (peace be upon him) prohibition of excessiveness in supplication. The Prophet (peace be upon him) is the first to enter and open Paradise, and he does not wait for children at its gate.