In later centuries the half-shekel was adopted as the amount of the Temple Tax, though, in Nehemiah 10:33–34, the tax is given as a third of a shekel. 
Exodus 30:13 This is what each one who is registered shall give: half a shekel according to the shekel of the sanctuary (the shekel is twenty gerahs), half a shekel as an offering to the Lord. NRSV
After the return under Nehemiah Jews in the Diaspora continued to pay the Temple tax. Josephus reports that at the end of the 30s CE "many tens of thousands" of Babylonian Jews guarded the convoy taking the tax to Jerusalem (Ant. 18.313).
The tax is mentioned in the New Testament when Jesus and his disciples were in Capernaum, and collectors of the temple tax (Greek didrachma) came to Peter and said "Does your teacher not pay the temple tax?" (Matthew 17:24). This is the spur for the miracle of the coin in the fish's mouth.
After the destruction of the Temple
The first Roman attempt to halt payments of the tax was made long before the Jewish War on account of customs controls. The Senate had forbidden the export of gold and silver but the Jews of Italy continued to pay the Temple tax. In AD62 L. Valerius Flaccus, governor of the province of Asia, issued an edict forbidding the Jews of his province from sending the tax to Jerusalem. After the destruction of the Temple in Jerusalem in AD70 a new Roman tax was imposed for taxation of the Jews, the Fiscus Judaicus diverted into imperial coffers.
- The Gospel of Matthew: Chapters 11-28 - Page 196 William Barclay - 2001 THE TEMPLE TAX Matthew 17:24-7 When they came to Capernaum, those who received the half-shekel Temple tax ... the basis of Exodus 30:13, it was laid down that every male Jew over twenty years of age must pay an annual Temple tax of ...
- Aaron Levine The Oxford Handbook of Judaism and Economics - Page 570 - 2011 with the twenty-gerah shekel that is mentioned in the Torah (e.g., Exodus 30:13). ... In later centuries the half-shekel was adopted as the amount of the Temple Tax (although, in Nehemiah 10:32–34, the tax is given as a third of a shekel).30 The ..."
- The Formation of the Early Church - Page 21 Jostein Ådna - 2005 "... by specially appointed envoys from communities all over the Diaspora. For example, Josephus reports that at the end of the 30s CE "many tens of thousands" (Ant. 18.313) of Jews in Babylon shared in the convoy of the Temple tax in fear of ..."