You have many asynchronous jobs but must run at most limit at the same time. A job here is a zero-argument async function, so nothing starts until you call it.

asyncio runs tasks on one thread. Tasks switch only at await.

import asyncio

async def main():
    results = await asyncio.gather(
        job_a(), job_b())
    return results

gather runs coroutines concurrently and returns results in the order passed in, not finishing order. If one raises, that exception reaches the awaiting code.

asyncio.Semaphore(n) is a counter of slots. async with waits for a free slot, and releases it on exit, even after an error:

sem = asyncio.Semaphore(2)

async def guarded(job):
    async with sem:
        return await job()

Call the job inside the async with, so its work only begins when it holds a slot.

Write async def gather_limited(jobs, limit) running zero-argument async functions with at most limit running at once, and returning their results in input order. An exception from a job propagates unchanged. Raise ValueError if limit is below 1.

The explanation opens here once every check passes.