I was praying for 1 month in the wrong direction (not toward the Qiblah). I used a compass, but it gave me the wrong direction. Do I have to repeat the prayers of that month or anything else?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

If someone prays to a direction which he believes to be the direction of the Qiblah basing his choice on a firm personal opinion or a compass and then finds that he prayed to a direction other than the direction of the Qiblah, then is not obliged to make up the prayer.  ‘Abdullah Ibn ‘Amer narrated that his father said: "We were with the Prophet on a trip during a dark night and we failed to know the direction of the Qiblah. So, each one of us chose a direction and prayed towards it. In the morning, we mentioned what happened to the Prophet . Then Allah revealed to him the following verse (which means): {So wherever you [might] turn, there is the Face of Allah.} [Quran 2:115]  [At- Tirmithi and Ibn Maajah]

However, if you were negligent in setting the compass or in knowing the code of the city where you are, then, in this case, you must make up all the prayers you had missed.

Allah knows best.