What is the modal verb of possibly?



Hello and thank you for the question.
The examples that you listed are already very good examples. Modal verbs of possibility are used when there isn't a 100% certainty that something happened. You can even use these modal verbs to speak about events in the past. Here are some examples:
1. She may have gone to the park.
2. She could've won the competition.
You'll notice that when we use these modal verbs to speak about past events, we use the Past Participle, 'gone' and 'won'.
I hope that this explanation and these examples help you!