The POSIX standard exists in different profiles, one of which is PSE51. It's a subset of the full POSIX profile, not requiring multiple processes (or threads), and not requiring file systems. PSE51 is the smallest subset, "Minimal real-time system profile" and is often used for the purpose that name indicates.
In addition to the usual POSIX specification, you can refer to the API Standards for Open Systems paper for the description of the various POSIX profiles. The paper has a "feature matrix" appendix, showing which APIs are included.
Adaptive AUTOSAR will become like Linux? File System, System Call and so on.
Adaptive AUTOSAR is POSIX-based, so it's like Linux in that broad sense. File systems are not part of PSE51. System calls are an implementation detail as far as POSIX is concerned, but using Linux as an example, many of its system calls are there for POSIX-specified functionality, so the same can conceivably be the case in Adaptive AUTOSAR.
Vendors are of course free to extend their implementations of Adaptive AUTOSAR beyond what the specification requires, so there could be vendor-specific multiprocessing or file system solutions.
In more practical terms, the relationship between Linux and adaptive AUTOSAR will likely be that adaptive AUTOSAR will be running within the context of Linux, for example, within a Docker container or such.