Flight Issue and Disappointment with THY

I arrived at Giresun Airport 40 minutes before (10:20) my 11:00 THY flight from Giresun to Istanbul with my child, but I was not allowed to board the plane. You can check the camera recordings for my entry time to the airport. I felt extremely embarrassed as my child was crying loudly beside me. It's really hard to describe the tears and sorrow I felt while talking to your customer representative, but you are the ones who put me in this situation. I will never choose you again for domestic or international travel. I know that in a previous flight, you waited for another passenger, delaying all other passengers. Unfortunately, as a decent person, I wasn't accepted in my own country, but if I had caused a scene, I might have been allowed on the plane. I didn't want to be rude. This is my last ticket with you. Additionally, you are not helping me with the next flight and are saying I have to pay the regular fare. Your customer representative just told me to file a lawsuit and ended the conversation. I want a refund.