WI: Leo VI has a son earlier

What if the Byzantine Emperor Leo VI had a son much earlier than OTL Constantine VII (from wife number 4)? Lets assume the child survives to adulthood and is reasonably competent (perhaps levels of OTL Constantine VII). What effect could this have on the Byzantine Empire in the short and medium terms, seeing that this likely eliminates Alexander III from becoming a big player and the power struggle between the Empress-mother and Patriarch Nicolas Mystikos? What is Tsar Symeon going to do if the Empire is in better hands in early tenth century? And what effects would the butterflying of Romanos I have?

Sorry, loads of questions-but this suddenly came to my mind and had to ask.
 
The only other son Leo VI had before Constantine VII was with his third wife, Eudokia Baiana. She died in childbirth in 901 and the child, named Basil, only lived a few days. If he survives and Leo VI dies on schedule, he would be 11 years old. It may not butterfly the reign of Alexander II or the regencies of Patriarch Nicholas Mystikos and Zoe Karbonopsina.
 
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