Logan could always be producing child 5 with his secretary.
I'd say Connor could become his favourite child, but only temporary and completely by default. But then again, I don't think Ken, Shiv & Roman have disregarded him for spite. I think Logan is responsible for all the dismissal of Connor. At the beginning of the show, we were told Kendall had been groomed since childhood by Logan to one day take over. Not Connor.
Questions I have before season 4:
1. Did Shiv fully realize that Tom stabbed her in the back?
2. Did Greg understand what Tom meant by selling his soul to the devil?
3. Is it over for Waystar Royco as a conglomerate if GoJo buys it?
4. Is Logan really ready to sell and just be a name without sole control?