Preferentially is the adverb: it tells you that something is done in a preferential way — not equally, but so as to give an advantage to particular people or things. A bank may lend preferentially to small shops; a school may admit local children preferentially; in science, a cell may take up one chemical preferentially. It is a formal, careful word, more at home in reports and papers than in chat. Though actually, everyday English often just says “they give preference to…” or “they treat X better,” and saves this long adverb for when the writer wants to sound exact. It always points back to that tilt: someone or something is being favoured on purpose. Do not mix it with preferably, which is a much more common word about what you would rather do.