In which OSI layer is the REST API paradigm?

REST architecture is stateless in a sense that the server does not store the state of the client, but state of the objects are transferred back and forth. After all, REST stands for Representational State Transfer. So, I'd think REST belongs to Layer 5 - Session Layer, which is commonly described as the layer where continuous exchange of information in the form of multiple back-and-forth transmissions between two nodes.

It's hard to see how REST API could belong to the Layer 6 or Layer 7 of the OSI Model. The Presentation layer provides for negotiation of the form of representation or syntax of the data that will be transferred. Usually mechanisms like character encoding (UTF, ASCII), data encryption and decryption are part of presentation layer. Application layer provides application specific services like FTP, HTTP, Telnet that support end user processes.

REST is not a protocol for two systems to communicate. REST is an architecture style. It is mostly atop HTTP, the application layer.