Q) US income tax applicable on US permanent resident working outside USA
I am a US resident arrived a month ago. I have a job outside USA which I may continue till I find a job in USA. I do not have any income in US.kindly reply to the above query. Thanks

U.S. residents have to report ALL world-wide income on their tax returns, so it does not matter whether the income is U.S.-sourced or foreign sourced.

What tax rebates are applicable to foreign earned income.

That depends on how you file (resident or dual-status), your marital status and whether you have children.

A U.S. citizen or resident must report worldwide income.
If you paid taxes in the foreign country, you will claim credit for taxes paid in the foreign country by filing Form 1116 or can file form 2555 Foreign Earned Income Exclusion.

Another filing requirement is Form TD F 90-22.1 and/or 8938 Specified foreign financial assets (SFFA). Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income