Will a Termination Show Up on a Background Check? Will it be harder for me to get a job if I receive an official termination letter from my previous company?

Recently I got terminated during my probation period. Does this mean that my next employer can do a background check on me to find out if I've been terminated if I sign the form that allows the company to do a background check on me? Will I have a lower employment chance if they find out that I got terminated then?

apparently, i did not get terminated but my boss forced me to resign. it's a digital marketing agency based in vietnam. when i got the job, no training was given. i was just told to bring in sales. when i make a mistake, they scold me without any reason. when i asked if they could teach, they would get angry and tell me to learn on my own. hence, they forced me to resign. i am currently unemployed and looking for a job. if someone here has a job, please do let me know