Yes, brother, in Islam this marriage can be permissible if there is no blood relation or foster (rada‘ah) relation between you and the girl. Your father’s wife’s daughter is considered your step-sister through marriage only, not through blood. In the Qur'an (4:23), Allah clearly mentions the women who are permanently forbidden for marriage. A step-sister from your father’s marriage is not included among the prohibited relatives unless she became related through breastfeeding (rada‘ah) or another direct prohibited relationship. Therefore, if she is only your stepmother’s daughter and there is no other Islamic barrier, then the marriage is generally permissible.
At the same time, Islam also encourages wisdom, family harmony, and careful consideration of emotions and relationships within the home. Before proceeding, it is important to involve elders, seek proper family understanding, and ensure that the marriage will not create conflict or discomfort within the family structure. Marriage is not only about permissibility, but also about long-term peace, compatibility, and respect. If both families are comfortable and the relationship is built upon deen, good character, and mutual understanding, then there is no sin in pursuing it in a halal manner.
May Allah guide you to what is best, bless your decisions with wisdom and barakah, and grant you a righteous spouse who brings peace, love, and closeness to Allah. Ameen 🤲
And Allah knows best.