Past simple with today
Solution 1:
If I found a ball in the morning, I might say in the afternoon I found a ball today. The past tense locates an action at a specific time in the past, but today is a sufficiently prolonged period of time to allow the use of the past tense on the same day. I have found a ball today could occur, but only exceptionally, because the perfect construction is not normally used when the sentence contains a specific time reference.
I find a ball today would be found only rarely and then only in a hypothetical sentence such as: Let’s suppose I find a ball today.