Hanuman Jayanti marks the birth of Hanuman, the devoted companion of Rama. In North India and in most of the diaspora it is kept on Chaitra Purnima, the full Moon day of the month of Chaitra, soon after Ram Navami. Devotees visit Hanuman temples, read the Hanuman Chalisa, offer sindoor and sweets, and many fast until the evening.
Not every region keeps the same day. Tamil Nadu, Andhra Pradesh, Telangana, Odisha and some other regions keep Hanuman Jayanti on a different day or in a different month. This page shows the widely used North Indian date, the Chaitra Purnima, and gives the time the Purnima tithi runs in each city. If your family follows a regional custom, use that day.
The date rule here is the civil day on which Purnima is in force at sunrise; if it is in force at the sunrise of two days, the first is taken. The Purnima tithi begins in the afternoon or night before and ends during the following day, so the beginning and end times in the tables are given on the clock of each city, with a note when they fall on the previous or next day.
Why do cities differ? The Moon reaches full at one instant worldwide. A city where sunrise comes before that instant sees the full Moon only at the following sunrise, while a city further east may already be past it. That is why two cities can list different dates in some years.
A calm note: the Hanuman Chalisa is short and can be read in a few minutes at any time of day. There is no need to worry about minutes of the tithi; it is the devotion that the day is about.