Airtable does not offer any record-level permissions, neither static permissions nor dynamically-changing permissions based on dynamic criteria.
The only simulation of record permissions that you can implement would be to use a filter to hide or show certain records. You can filter your interface to show a user only their own records, or you can filter based on other criteria.
For anything more advanced than that, you would need to pay extra money to use an Airtable portal.
A few of the leading customer portals are Noloco, JetAdmin, Softr, Pory, and Glide.
JetAdmin is probably my favorite for sheer simplicity & user-friendliness, while Noloco is probably the most powerful & customizable one.
I give a brief tutorial of Noloco on this Airtable podcast episode. And I also presented a full one-hour webinar on Noloco called Building a Client Portal on Noloco powered by Airtable.
If the portals don’t support all the features that you need, then you would need to look at more advanced database apps that offer record-level permissions as a key security feature of the product. The best database app that I know of that offers this is FileMaker.
I used to be a FileMaker developer for 30 years before becoming an Airtable consultant. If you go down the FileMaker path, feel free to reach out to me through my website and I can put you in touch with some great FileMaker developers.