Electric fireplace equipment does not need a lot of regular routine maintenance. Keeping the batteries fresh in the remote probably tops the list. Most require AAA’s.
Cleaning the kids’ fingerprints from the glass can be done with a common household glass cleaner using a non-abrasive cloth. Let the glass thoroughly cool before cleaning.
And, if you have dogs or cats in the house, make sure the fireplace is kept free of pet hair and dust bunnies. Use a vacuum with a soft brush attachment to gently remove any dirt, dust, lint or other debris from the vent openings and control areas of the fireplace.