I'm kinda new to Kubernets and I think I understand the basics of the whole system but most of the stuff I have read was about how to use kubectl to start a service and deployment and stuff.
But in my use case I have this web API running (built in ASP.net core) that takes a request, does some processing and depending on the input data has to start a secondary process.
A Kubernetes job with restart policy OnFailure seemed to be the way to implement those secondary processes but I can't find any resources on how the web server can be used to start this job.
You can use Kubernetes API to create a Job(or any kubernetes resource) from your application running inside the cluster. You can either install kubectl inside your applications's container and call it from your application code or use a kubernetes client library(https://github.com/kubernetes-client/csharp) to talk to kubernetes API server.
See the following answer for more details:
Kubernetes - Finding out how many replicas there are in a service?