Is there any way in C# that I can limit the range of an int variable?

No. This is a good example of why exposing public fields is a bad idea - you have no control over how they're used.

If you change it into a property, you can validate the value in the setter:

// TODO: Use a better name than either foo or aBtn
private static int foo;

public static int Foo
{
    get => foo;
    set => foo = value >= 0 && value < 6
        ? value
        : throw new ArgumentOutOfRangeException("Some useful error message here");
}

If you don't like using the conditional ?: operator there, you can use a block-bodied setter:

public static int Foo
{
    get => foo;
    set
    {
        if (value < 0 || value > 5)
        {
            throw new ArgumentOutOfRangeException("Some useful error message");
        }
        foo = value;
    }
}

Or better, have a utilty method that validates a value and returns the input if it's in range, or throws an exception otherwise. You can then use something like:

public static int Foo
{
    get => foo;
    set => foo = Preconditions.CheckArgumentRange(nameof(value), value, 0, 5);
}

Here's a slightly modified version of CheckArgumentRange from Noda Time. (The real version has a separate method to do the throwing, which I suspect is for performance reasons, to allow the comparison part to be inlined.)

internal static int CheckArgumentRange(
    string paramName, int value, int minInclusive, int maxInclusive)
{
    if (value < minInclusive || value > maxInclusive)
    {
        throw new ArgumentOutOfRangeException(paramName, value,
            $"Value should be in range [{minInclusive}-{maxInclusive}]");
    }
    return value;
}