APA suggests ensuring you describe how you used the AI tool in your research in a method section or comparable section of your paper.
APA also suggests that given that AI generated content like chats are not created by a person, that they cannot be considered personal communication. Instead, treat the content as an algorithm's output, and credit the author of the algorithm with a reference list entry and in-text citation.
You can also put the full text of long responses in an appendix or online supplemental materials.
References:
Author. (Year of the Version). Title of the Tool (Version if applicable) [Tool description if applicable]. Source/URL
Example:
OpenAI. (2023). ChatGPT (Mar 14 version) [Large language model]. https://chat.openai.com/chat
In-text Citation:
Parenthetical citation: (OpenAI, 2023)
Narrative citation: OpenAI (2023)