Great question!
"It was morning," "It was Sunday morning," and "On Sunday morning" are commonly used in both spoken and written English.
"It was a morning" is typically used to tell stories, especially in books, to create a scene or set a mood.
For example:
"He called me on Sunday morning." → More informal, commonly used in everyday English.
"It was *a* cold Sunday morning, and the world outside was covered in a blanket of snow." → More descriptive and artistic, often used to tell a story.
I hope this helps!