I want to use nClam (https://github.com/tekmaven/nClam), a library for antivirus scanning with .NET core 1.1. The library currently requires .NET core 2.0 but it looks like I can work around this with a few light modifications to the nclam.csproj file. Since I can't use NuGet, how can I add the modified source code to my project?
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There are 2 ways you could go about doing this:
If you are building locally and shipping the compiled version (no build server involved), you can definitely use nuget. You can setup a folder on your local environment as a nuget source: just use the "manage nuget packages" for your project in Visual Studio, click the gear icon and add the folder that has the modified nClam nuget. You can create the nuget using dotnet pack or the checkbox in the nClam project settings to create the package on build.
You could always load the project into your solution and add a reference to it from your project. All references to it will just then work, and no nuget package is involved

You don't install a NuGet package via source code. NuGet packages can only be "installed" via a NuGet server. You make the claim, "I can't use NuGet" so you have nothing to do with NuGet. You can either clone the repository (using git) or download the repo zip.
Once you downloaded the source (and perhaps extracted it), you can copy over the project to your code base. Then add an existing project to your solution and reference it with your modifications.
As the maintainer of the library, I would recommend you take a source dependency on the library. The majority of the code is in
ClamClient.cs
. The library is extremely stable and the fundamental source code of the library has not changed since its creation in 2011. The majority of changes are just to maintain the library as the .NET ecosystem evolved (async, .NET Core, etc).When/if you upgrade the project to support .NET Standard 2.0, you can switch back to a package reference.