1) Conceptual impossibility-impossible by definition.
2) Logical impossibility-if an assertion that something has been done results in a contradiction, regardless of how one defines the terms used in the assertion.
3) Factual impossibility-things are impossible based on the known structure of reality.
4) Normative possibility-a form of possibility that involves rights and duties (i.e. employees and employers each have prescriptive responsibilities toward one another by means of some formalized agreement).
Some things clearly appear to be factually, conceptually or logically impossible like square circles or events that have happened, then unhappened (Nicomachean Ethics 6.2). Nothing is also red and green all over: that too is factually impossible. Nor is Lebron James both taller than 6 feet and not taller than 6 feet at the same time and in the same respect (law of noncontradiction).
God does not do things that by their very nature are impossible; otherwise, we land ourselves in many contradictions.
Is it possible for God to sin or act unjustly? Is it possible for God to be tempted or tempt anyone with evil things? See Titus 1:2; Hebrews 6:18; James 1:13-15
Can God create a universe that has always existed? Or is a universe that has always existed by its very definition uncreatable?