If your child is under 12 and is being privately educated at a fee paying school in the UK you can apply for a Parent of Tier 4 Child Visa.
This will enable you to live here with them.
You need to show that you will return to the country after your visit and that you have sufficient funds to support yourself in the UK.
Initially a visa would be granted for 6 or 12 months and extensions of 12 months at a time can be granted until the child reaches 12 years of age.