Mi madre quiere que yo (regresar) a casa.
a. regreso
b. regrese
c. regresa
d. regresó

Regrese is the correct answer, remaining the full phrase as follows: Mi madre quiere que yo regrese a casa.

Explanation:

Regrese is conjugated for the first person in the subjunctive form (modo subjuntivo), which is used to express wishes, petitions or possibilities. The words regreso (option A) and regresa (option C) are written in the present tense of the indicative form (modo indicativo) in the first and third persons respectively. The word regresó (option D) is written in the past tense of the indicative form of the third person.

As the phrase is indicating the wishes of a person for someone to return home, then the right form to use the verb is not present tense of the indicative form nor in past tense, but in the subjunctive form, as it expresses possibilities or wishes, as found in option B.