Lied about job employment

To preface I’m not looking to be over-employed just getting back into the workforce. people didn’t like my post in the normal subs.

I am wondering if this will get me rejected.

My first job out of college was a for a small marketing firm. I worked directly with the founders and it was definitely a small business type of role. They didn’t seem to know where things were headed and I was frustrated because we were giving small business clients poor results and charging them 3k a month so I quit at about 4 months in. I did have a W2 but they ended up switching paystub processors right when I left. they couldn’t even find my tax forms…

So on my resume I put that I was there for 12 months.

Will this hurt me? And can employers immediately tell from a background check?

This is my second job experience listed on my resume as my first was my own service based business I started and sold for about a year.