Q. When should machatzis hashekel be given this year, on Taanis Esther (Thursday) or Motzei Shabbos (Purim)?

A. There are different opinions and traditions as to when to give machatzis hashekel. Rema (694: 1) maintains that the minhag is to give machtzis hashekel before Mincha on Ta’anis Esther. Mishna Berura (ibid.:4) affirms this minhag. Piskei Teshuvos (694: 3) quotes Luach Eretz Yisroel to give it after Mincha. He and Kaf HaChaim 694:25 maintain that it should be given on Ta’anis Esther even if the ta’anis is advanced to the previous Thursday. This is done in order to donate tzedaka on the fast day.
As the Talmud teaches (Brachos 6b) that the reward for a fasting day is the charity given.
However, Chazon Ovadyah (Purim pg 101) and Piskei Teshuvos (ibid.) opine that the minhag is to give it before the reading of the Megilla, the reason is founded on the Talmud (Megillah 13b) that mentions the reason of donating our shekalim in Adar is to counteract the shekalim given by Haman.
Therefore Nitei Gavriel (Purim 8:1) quotes from Darkei Chaim Vesholom and Shefa Chaim that when Purim is on Sunday, the machatzis hashekel should be given twice, on Ta’anis Esther and on Purim day before megilla reading.
Horav Shlomo Miller’s Shlt’a opinion is that one should follow the minhag of his family or community. However this year, it is better to give it on Thursday a weekday when money is available and you comply with the mitzva earlier.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a