Class Design with Generic Class and Interface in C#

I am working on an old piece of code and trying to implement it afresh with the new advancements in .NET. However I can't wrap my head around the design for the same. Previously there were no template classes/interfaces and now I need to make use of the same. I will try to give an example of the design and where I am getting stuck. The design is something like this :

interface Service<T>
{
    T Value;
    Task AsyncWork();
}

class Input<T> : Service<T>, Input
{
    Worker w1;
    Task AsyncWork()
    {
        w1.WorkOnInput(this); //error
        ... //will return a Task eventually
    }

}

class Input
{
    //common members and methods for child classes
    int priority;
    string Name;
    FormatInput()
    {
        //some common implementation
    }

}

class StringInput:Input<string>
{
    //Implementation specific to string input
}

class IntInput:Input<int>
{
    //Implementation specific to int input
}

class Worker
{
    WorkOnInput(Input)
    {
        ...
    }
}

Main()
{
    Worker w = new Worker();
    Input input1 = new StringInput();
    Input input2 = new IntInput();
    input1.FormatInput();
    input2.FormatInput();
    List<Input> inputList = new List<Input>();
    inputList.Add(input1);
    inputList.Add(input2);
    AnotherMethod(inputList); //another method which expects a list of Inputs
    w.WorkOnInput(input1);
    w.WorkOnInput(input2);
}

I cannot change the interface implementation as I am not the owner of the same. But as the comment shows I would have an error at w1.WorkOnInput(this), since this here expects Input type and not Input<T>.

However if I change the WorkOnInput to accept an argument of type Input<T> then I would have to make it a generic method as WorkOnInput<T> and if I would need to call it I would explicitly have to provide the type of the input which is also not desirable.

Also I have a list of inputs which is needed to be passed to AnotherMethod() and a List<Input<T>> is not possible.

I think I am getting a bit too confused with the scenario and am going round and round without any concrete solution.

Can someone please point me into the right direction?