Touching mushaf while in minor or major impurity?

Is this a sin?

as-salamu alaikum,

you cannot touch the mushaf while being in the state of major impurity,
it is stated in al-Mukhtasar al-Mufid:

It is forbidden for anyone in this state to:
— Recite (the Qur’an) with the tongue,
— Write it, even a part of a verse,
— Touch the muṣḥaf (the physical Qur'an),
— Enter the mosque,
and a man who has ejaculated must urinate before performing the ritual bath (ghusl).

If you do it while being in that state, than you have sinned.

wa salam

what about minor impurity?

minor impurity is only a hinderance for establishing the prayer.

As for reading or touching the Quran it is allowed and not a sin
according to the relied upon position in our school.