What should a husband do if he wants to divorce his wife after a four-month marriage, contracted Islamically but unrecognized in Germany, and the wife refuses reconciliation, and the husband claims that what is happening is sorcery and witchcraft, confirmed by a ruqyah-performing imam, while the wife's father refuses to hear about matters of sorcery and ruqyah?

A woman is not permitted to seek a divorce without justification, and if she does, she is committing a sin. Try to convince your father to agree to the ruqyah (definition) shar'iyyah (Islamic exorcism/healing through Quranic recitation); if he refuses, seek the help of some scholars and people of virtue. If you insist and wish to divorce her, you are entitled to do so. If you wish to seek a khul' (divorce at the wife's instance, usually by returning her mahr or other consideration) in exchange for what you paid her, you are also entitled to that. The Islamic marriage contract is what is valid and gives rise to its legal effects, while the lack of legal registration has no bearing.