I have a goodman gas furnace, gms91155dxa for about a year. Recently I notice the furnace repeats on and off while it didn't reach at set temperature. After the heater is on, it runs some minutes and it shuts off itself. And the draft inducing motor runs, the ignitor is on and gas blows and in seconds with clicking sounds gas as well as draft inducing motor shut off.
And soon it repeats over and over again. What could be wrong,,

It sounds like it is overheating. Check filters, evaporator coil, or anything else stopping air flow.

Thank you for your kindly advice, I checked the filters. I guess I need to speed up the blower motor or somehow reduce the gas flow by adjusting gas valve.

Is this the first time you have used the heat from this furnace or have you recently replaced the thermostat? The reason I ask is that a thermostat has an amperage setting on it that has to correspond with the gas valve of the furnace.
This is just one idea of what the problem might be. Take the face plate off the thermostat and look for a thing that has some numbers on it, these numbers will run from something like .03 to 1.05. On this scale is a slide that will move from one number to the next. On the gas valve in the furnace there is a amp rating (this will be probably be printed on the side of the gas valve. The number will look something like this 0.05, but it can be any number. When you find this number then go to the thermostat and set the slide to the corresponding number on the scale. This is called a heat anticipator and if it is set wrong the little coil of wire you might see heats like an electric heater and your thermostat thinks your house is warm but it cools off very fast therefore thinking that the house is now cool.
Let me know if you find what I am talking about and also if it solves the problem. There could be other causes.