Accidentally invested into a Roth IRA but make over the amount allowed to contribute

Hi! I’m not great at anything investing related so really hoping for some advice here.

I used to make around $83k a year so I decided to invest in a ROTH IRA and contributed $6k which was the max you were allowed to contribute at the time. I ended up getting a new job that same year and started making over the income limit. While filing my taxes I was told I needed to remove x amount of money from my Roth IRA (it was around 3K) and was allowed to keep the rest in since I only started making over the income limit for half the year. I then removed that amount and paid the penalty the following year in taxes. I now still have that $3kish amount I was allowed to keep in and it’s grown to around $4k but I’m not sure what to do with it since I can no longer contribute.

So either I can let that money just sit there and grow but what’s the point of just having that little amount in there till I’m at the age where I can removed it without a penalty or should I remove it and pay the penalty for removing money from the Roth IRA before you are 60.

I’ve also heard of back door Roth IRA but not sure how that works and if i qualify but please let me know what I should do! Thanks so much 🙏🏾