ASP.NET itself won't be able to run on Apache web server because it is strictly tied to the components and services provided by IIS on Windows. This means, a dead end here. Anyhow, you can still consider using Mono Project and compile your ASP.NET web app against Mono, that can be worked against Linux or other platforms, and other web servers too. This is what I found for you,
mod_mono | Mono[
^]. You can check the documentation and then make required changes to deploy the web app on Apache servers.
ASP.NET Core supports Apache and other servers quite well. So you can consider that framework if you want to use Apache. See this for example,
Host ASP.NET Core on Linux with Apache | Microsoft Docs[
^]
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