In many parts of the Muslim world people claim to be descendants of the Prophet. Generally these are Sayyids:
Sayyid (سيد) (plural Saadah) is an honorific title that is given to males accepted as descendants of the Islamic prophet Muhammad through his grandsons, Hassan and Husayn, who were the
sons of his daughter Fatima Zahra and son-in-law Ali ibn Abi Talib
Are the people who claim to be Sayyids really Sayyids? If they share common descent from Ali, their Y chromosomal lineage should be the same. Or, more likely assuming a small proportion of infidelity per generation you will have one modal Y lineage, and a host of other alien lineages at much lower frequencies.