Try to use DispatchSemaphore.

concurrency.swift

class Controller {
    var isProcessing = false
    let semaphore  = DispatchSemaphore(value: 0)

    func doit() async {
        do {
            print("try")
            semaphore.signal()
            if isProcessing {
                print("busy")
                semaphore.wait()
                return
            }
            isProcessing = true
            semaphore.wait()
            try await Task.sleep(nanoseconds: 1000000000)
            print("doit")
            semaphore.signal()
            isProcessing = false
            semaphore.wait()
        } catch {
            print(error)
        }
    }
}

var con = Controller()

Task {
    await con.doit()
    task.cancel()
}
Task {
    await con.doit()
}
Task {
    await con.doit()
}
Task {
    await con.doit()
}

let task = Task {
    do {
        try await Task.sleep(nanoseconds: 2000000000)
        await con.doit()
    } catch {
        print(error)
    }
}

Task {
    try await Task.sleep(nanoseconds: 4000000000)
    task.cancel()
}