I swore by the Quran not to do something, then did it. What is the expiation for swearing by Quran?

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.

The Muslim scholars have two opinions regarding a person who swears by the Quran and then breaks it.

The majority of the Muslim scholars are of the view that whoever swears by the Quran [and breaks it] is obliged to expiate for breaking his oath, just like other oaths. This is the most correct opinion. But some other scholars are of the view that he is obliged to expiate for every verse in the Quran.

Imaam Ibn Qudaamah said: “If we oblige one to expiate as much as the number of verses in the Quran, then he can not perform it; so paying one expiation is sufficient for him”. [Meaning only for breaking the oath].

The expiation of breaking an oath is feeding ten poor people or clothing ten needy people, giving each one the cloth which covers the Awrah (those parts of the body which must be covered in Islam), or freeing one Muslim slave. Whoever can not do any of these should fast three days. Allah Says (what means): {Allah will not impose blame upon you for what is meaningless in your oaths, but He will impose blame upon you for [breaking] what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever cannot find [or afford it] — then a fast of three days [is required]. That is the expiation for oaths when you have sworn. But guard your oaths. Thus does Allah make clear to you His verses [i.e. revealed law] that you may be grateful.}[Quran 5: 89].

As for putting one’s hand over the Quran while swearing, then this is only to confirm and strengthen the oath not more, so it does not have any effect on the expiation of the oath.

Allah knows best.