I have a beckett afg oil furance when I hit the reset button it lite run reach the temperature in the house but when temparture drop in the house the furance will lite but cut off when try to startup again it lite but just go out

Make sure you have plenty of oil in the tank.
Many problems can cause what you describe.
When was the last time you have a professional tune up?
This should be done every year!

Oil furnaces are a little different from most of the gas oriented info at https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html

You still need to follow the same steps, identifying the last step that happens and checking the sensor for it and if the component in the next step is getting power.