Will anything befall me for having sworn to my mother on the Quran present on my mobile phone, concerning not severing ties of kinship, and then regretting this oath?

It is not permissible to swear an oath except by Allah or by one of His attributes, such as the Qur'an. Swearing by the Mus'haf (physical copy of the Qur'an) is permissible if what is intended is the speech of Allah, and it is not permissible if what is intended is the paper and ink.

Whoever swears by the Mus'haf on a mobile phone and intends the speech of Allah, then their oath is a valid oath (yamin), and lying in it is a grievous oath (yamin ghamus). However, if they intend to swear by the page or the application, then it is not an oath, and they must seek forgiveness for lying and for swearing by other than Allah.

It is not a condition for the validity of an oath to place one's hand on the Mus'haf or open it. Whenever one says "By the Mus'haf" and intends the speech of Allah, it is a valid oath. A Muslim must not swear by the Torah or the Gospel due to their corruption and because Islam abrogates what preceded them.