Turkish Airlines Flight Boarding Issue

Hello, I experienced an issue with my Turkish Airlines flight (PNR VQ74YV) on 05/01/2024 at 13:30 from Istanbul Airport to Agri Airport. Despite completing check-in at 13:00 for 2 adults, 2 children, and 1 infant, we were denied boarding because we were 3 minutes late. When we arrived at the gate at exactly 13:13, the staff informed us that the gates were closed and we would not be allowed to board. We tried to explain that we needed to board due to a family funeral, but the staff firmly stated, 'No one can let you on this flight, there is nothing I can do.' Detailed footage can be obtained from the camera recordings. Even though we checked in, no announcement was made, and when we mentioned this to the staff, they said announcements are not made. Other relatives on the same flight tried to alert the staff, but they dismissed it by saying, 'Since they checked in, they will definitely board.' We had to purchase new tickets for the next day and pay an additional fee. We were significantly inconvenienced both financially and emotionally by Turkish Airlines. I urgently request that this issue be resolved.