How to setup a .NET core web api that

* accepts a string value,
* puts into a queue
* and return flag that message is accepted (regardless it is processed).

Also, a routine which keeps checking the queue, and process the messages one by one. 

As per the requirement, the api is going to act as the receiver of messages which may get hits as much as hundreds of times in a minute, while the messages it receives should be processed one by one.
I am bit new to web apis, so wonder if such setup is good to have and if yes how to put together different components.

Thanks in advance..