How can you block/reject subdirectories only, with an irule?

Hello,

Ok, you just need to replace "*/appsite1" by "/appsite1" to make it works your way.

when HTTP_REQUEST { 
    switch -glob [HTTP::path] { 
        "/appsite1" { HTTP::respond 403 content "some html content explaining that the request is not allowed" } 
    } 
}

and if you don't plan to add exceptions, you can use a simple if condition

when HTTP_REQUEST { 
    if { [HTTP::path] equals "/appsite1" } { 
        HTTP::respond 403 content "some html content explaining that the request is not allowed"
    } 
}