Is it permissible for a traveler, if Friday prayer overtakes him in one of the cities, to pray Friday prayer with the residents and then stay and pray Asr?

There is no evidence for the permissibility of combining the Asr prayer with the Jumu'ah prayer, and this has not been reported from the Prophet (peace and blessings be upon him) nor from his Companions. Therefore, it must be abandoned. Whoever does so must repeat the Asr prayer when its time enters.