According to Walter M. Spink’s timeline, Ajanta Cave 1 was developed from circa 466 to circa 477 CE.
There is no direct evidence available to answer this question. However, a noted scholar, Walter M. Spink, has argued that the Ajanta Cave 1 was most likely patronised by the Vakataka Emperor Harisena who was ruling at the time when the fifth-century cave temples of Ajanta were being developed.
There are 15 narrative paintings in the Ajanta Cave 1. This is the number according to the corpus of the noted scholar Dieter Schlingloff. He has researched exclusively on the Ajanta narrative paintings. He has indexed all the narrative paintings of all the Ajanta caves. This list of course is based on what has come to down to us in the modern times. Many of the ancient paintings have been damaged, decayed, or permanently lost.
According to the published investigations by Walter M. Spink, the Ajanta cave 1 was never put to worship. It was abandoned even before the full completion, just before the dedication ceremony could take place.