Which extinct creatures were most genetically distant from everything alive today?
The very first ones to go extinct would be the most genetically distant; at that distance, the issue becomes more "how do you define life?" or "how do you define a species?" to get the actual most distant. Overall, it sounds like an interesting question, but it really isn't: extinction isn't special, it's the norm. There are most certainly extinct organisms or pre-organisms of some level of development that never contributed to the existing life on earth and have no descendants or relatives.