I am not a US Citizen and nor a greencard holder, I do not live in the united states anymore, but i do have an american child do I need to pay taxes?

[ritalopo]

I am not a US Citizen and nor a greencard holder, I do not live in the united states anymore,

[Opus 17]

As a non-resident alien, you are only required to file a US tax return if you have US-sourced income.  

Most of the time, wages are considered sourced to where you actually performed the work, even if the employer was based in the US.  And most of the time, capital gains and dividends from stocks and bonds are not US source income even if the company or exchange is in the US.  US source income might include sale of property you owned in the US, or business profits if you are an active participant (not just a shareholder) in a business or partnership.  There is a table here.

https://www.irs.gov/individuals/international-taxpayers/nonresident-aliens-source-of-income

Lastly, note that if you do have US-source income and don't report and pay tax on it, the IRS may have no way to collect from you, but that will be a mark against you if you ever intend to return to the US.