It is not permissible to combine 'Asr with Jumu'ah.
Because the sunnah only mentions combining Dhuhr and 'Asr.
And Jumu'ah is not the same as Dhuhr. Jumu'ah is an independent prayer with its own status.
That is why it is only prayed in one mosque.
It is two rak'ahs, and the recitation is done aloud.
It is preceded by two khutbahs, and it has its own characteristics, and it is only valid in its time. It has many unique features, so it cannot be considered the same as Dhuhr.
And by analogy to that, combining 'asr is allowed.
This applies to the traveler, a traveler or a sick person, for example, who attends jumu'ah.
We say no, it is not obligatory. Jumu'ah is an independent prayer, it has no equivalent among the five daily prayers.
So 'asr is not combined with it.
And whoever combined 'asr with it should repeat the prayer, he should repeat the 'asr prayer.