Is there a specific prayer performed between Dhuhr and Asr on Friday?

There is no specific prayer between Dhuhr and Asr on Friday except for the post-Jumu'ah regular prayer (ratibah), which is authentically reported to be two rak'ahs at home, or four rak'ahs as commanded by the Prophet (peace be upon him), or six rak'ahs as performed by Ibn Umar (may Allah be pleased with them both). The most complete approach is to vary between these options. Some scholars are of the view that if one prays in the mosque, one prays four rak'ahs, and if one prays at home, one prays two rak'ahs.