I was hospitalized and doctor didn't allow me to fly, shall I get the refund? It was Turkish Airlines. We were four in the family. Since I was not able to fly, they couldn't.
I hope you're feeling better now. See the closely related question, I bought a flight ticket, but now I have a health issue which specifically forbids me to take flights. Can I get a full refund?
If you've purchased travel insurance, review your policy to see exactly what's covered and make a claim, as this is one of the main purposes of travel insurance.
Beyond that, unless you've purchased a refundable fare, the airline has no obligation to give you a refund. Most Turkish Airlines fares even say refunds are "NOT PERMITTED EVEN FOR MEDICAL REASON" in their conditions. As a customer service gesture, they may be willing to give you a refund or a partial refund. They may refund only the taxes. They may also allow you to move your travel to another date and might waive applicable change fees. They may make an exception to their policy for just your ticket and not the others. All of this is much easier if you request it before your travel dates, and much less likely if you call after you were already supposed to depart.
Assuming you have a ticket which does not allow for general refunds at all times, or in other words you have a ticket which restricts refunds altogether or restricts refunds to any point before the date of travel, its unlikely that you can claim a refund.
Having looked at the Turkish Airlines General Conditions of Carriage, I cannot see any clause which would cover refunds in the case of illness or other medical reasons for inability to travel, so there is no automatic right of refund in this case - you can discuss the matter with Turkish Airlines customer services, but they are under no obligation to refund the tickets.
You may be able to claim on any travel insurance you took out, depending on the level of cover and the specific policy, but you might be in a difficult position by not contacting them when your entire family made the decision to not fly - that is often something the insurance company would want to discuss, and they may not cover the voluntary decision to not fly differently over the involuntary decision to not fly.
Again, depending on the class of ticket you purchased, you may be able to request Turkish Airlines hold a credit of the residual value of the ticket, if any exists, for application against future travel. Many airlines consider a ticket to still have value in some circumstances even if the travel date has passed.