If you're wondering if your kid might have something extra special going on, you're probably right. Just the fact that you find yourself here asking these questions is an indicator in and of itself.
Intuitive, empathic, psychic, medium and highly sensitive kids can exhibit a variety of signs that they are operating with additional gifts. I'll go over some of the most common indicators of an intuitively gifted child. Your child may have one or all of these signs. Having only one indicator is not a sign of less powerful abilities however.
Past-life remembrance. These occur generally from age 2.5-3 (or whenever your child becomes verbal enough to explain themselves). These memories can range from simple comments about their "mom from before" or a recollection of where they used to live, all the way to detailed memories of their life and death. If your child shares their past-life stories with you, be sure to remain open and try not to take it personally if your child is experiencing grief or longing for their old family. It may take them awhile to integrate, but generally around age 5 we see a full integration into the current timeline (there are exceptions to this however)
Womb-time remembrance. Similar to past-lives you may find your child remembers their time spent in utero (my son let me know there was "lots of juice"). This is an indicator that your child consciousness was hyper aware from early on.
Recurring nightmares or night terrors. Sometimes if kids (or adults) attempt to shut down their psychic receiving, they can find a surplus of activity in their sleep time. Our energy fields are also smaller during sleep, so kids with dark-force energy contracts might feel that heavy energies have better access to them.
They see things. When psychic kids are small, they are generally protected (as all of us are) by our spiritual guides, angels, loved ones etc. These energies help to hold the space and keep us psychically safe from entities. However if you have a child gifted with clairvoyance they may still be able to see energies that exist outside of their field which can sometimes be scary. Kids with clairsentience (feeling) or empaths may seem extra sensitive to things they can't see but can sense or feel. Do your best to listen to their fears and support them energetically. I wrote a children's book just for this situation called Isabelle Brave which you can get HERE to help teach sensitive kids how to implement energy tools to ease their discomfort and calm their fears.
Staring at empty spaces in the room in infancy. This one is pretty straight forward and is particularly common in kids with mediumship skills. They are particularly attuned at seeing past loved ones visiting.
If you want to find more ways to support your intuitive child, I suggest checking out my class Raising Your Intuitive Child. Register or get on the waitlist HERE
I also offer 1:1 sessions with children 6 and older as well as family sessions and individual parent support sessions. You can book in 60 minute increments HERE