As a parent I understand your situation. depending on your child's age you could have him/her doing some school related work or art in his/her room while you get some work done.
You can go to bed just about the same time as your child and get up an hour or an hour and a half earlier and study.
Always have your notes or electronic device on you so that you can make use of each free minute you have.
Let me know what else you have tried doing thus far, because I have also only recently started and i am a parent, the few ideas have helped but there is always room for improvement.
