.net core dependency injection

There is currently no support for using a factory with an open generic type. There's an open issue on GitHub discussing this:

Dependency Injection of Open Generics via factory · Issue #41050 · dotnet/runtime · GitHub[^]

I'd suggest using another class to inject the parameter into your constructor. For example:

public class MyContextOptions
{
    public MyContextOptions(string value)
    {
        Value = value;
    }
    
    public string Value { get; }
}

public partial class MyContext<TEntity> : IMyContext<TEntity> where TEntity : class
{
    public MyContext(MyContextOptions options)
    {
           
    }
}

services.AddSingleton(new MyContextOptions("connection"));
services.AddScoped(typeof(IMyContext<>), typeof(MyContext<>));