Is it permissible for a sheikh to place a piece of a child's clothing on which to recite the Qur'an as a form of protection? And is this considered ruqyah or an innovation that should be avoided?

Ruqyah (definition) is legislated and recommended. It involves reciting over the patient, or blowing on them, or on water, oil, and similar substances, or by writing Quranic verses and washing them off with water for the patient to drink or bathe with. There is no harm in reciting over a child's clothes or anyone else's, as the scope of Ruqyah is wide, and there is no objection to relying on experience in it, as long as it does not involve shirk (definition). It has been proven that taking a trace from the envious person (al-ain) and using it is beneficial, so it is not far-fetched that reciting over a child's clothes would be beneficial, even if the primary approach is to perform Ruqyah directly on them or for them to drink water over which Ruqyah has been recited. The trace should only be given to someone whose religiosity is trusted, so that it is not used in magic.