Does covering the head after beginning to shave and before completing it necessitate a fidyah, or does beginning to shave release one from the state of ihram?

First: Covering the head is among the prohibitions of Ihrām for men, due to the Prophet (peace and blessings be upon him) saying concerning the deceased Muḥrim: "Do not cover his head," and his (peace and blessings be upon him) prohibition of wearing turbans for the Muḥrim.

Second: Scholars differed on the sufficient amount for shaving or shortening the hair. The Hanafis held that shaving or shortening a quarter of the head is sufficient. The Malikis and Hanbalis maintained that shaving the entire head is necessary. The Shafi'is held that three hairs are sufficient.

If the action was done out of ignorance or misinterpretation, then nothing is required of you. However, if it was done with knowledge of its prohibition, then you owe the fidyah for harm (slaughtering a sheep, or feeding six needy persons, or fasting three days), and your ʿUmrah is valid.

Those who commit prohibitions fall into three categories: one who commits it out of necessity, upon whom is the fidyah; one who commits it forgetfully, ignorantly, or under compulsion, upon whom is nothing; and one who commits it without excuse or necessity, who is sinful and upon whom is the fidyah. The most likely is that nothing is required of you.