Currently the Catholic Church honors St. Joseph on two principal feast days: March 19 and May 1.
However, historically these are not the only days the Church has honored St. Joseph, as there have been a variety of days the Church instituted to venerate the foster father of Jesus.
Third Sunday after Easter
The Carmelite Order honored St. Joseph on the Third Sunday after Easter, and this feast eventually spread to various dioceses throughout the world.
Dom Prosper Gueranger explains the history of this particular feast in his Liturgical Year.
A Sunday was selected for the celebration of this new Feast in order that the Faithful might be in a way compelled to keep it; for the Feast of St Joseph in March is not a day of obligation for the universal Church and, as it always falls during Lent, it cannot be kept on a Sunday, since the Sundays of Lent exclude a Feast of that rite...The new Feast went on gradually spreading from one diocese to another till at last there was unexpectedly issued an Apostolic Decree dated September 10, 1847 which ordered it to be kept throughout Christendom.
Third Wednesday after Easter
However, when St. Pius X initiated his own reforms of the calendar in 1912, he decided to remove it from the Third Sunday after Easter and to place it on the Third Wednesday after Easter.
It was fitting to place this feast on a Wednesday, as Wednesdays were traditionally a day when St. Joseph was honored, similar to how Saturdays became a day to honor the Virgin Mary.
This feast of St. Joseph remained on the calendar until 1955, when the Solemnity of St. Joseph the Worker was instituted on May 1.