Want To Abscond, Is It Fair

Hello Sir/Madam,
I was working with a company for 1 year, could not serve my notice period so i payed for notice period and left. Then Joined other company, worked for 2 years and left systematically. Now i joined the previous company back and suddenly got an offer from a better company with better package now i ve to abscond becoz the new company wants me to join immediately. please advise. If the new company does a background verification, will my previous company reveal that i joined back and absconded now. Give me a better option because i don't want to leave this opportunity.
In a very bad mind state, please help.
Thanks in anticipation,

If you are really keen to go with the new offer then the only option is leave systematically again, follow their exit procedure and resign.

I m not in a position to serve the notice period I ve to join in 5 day.. how s a background verification done?? Will the new employer call all my previous companies and ask the details

Will the new employer ask your existing company or not? No one can give definite answer. But, most probably they would do a BGV. You would be marked an absconder in present company and same would be shared.

If you are not in a position to serve the notice period then pay the notice in lieu of notice period.
Your new employer will do BGV or not that is something which depends on your new employer, how can we answer that.

Its only been 10 days I ve joined this company I m in training and I ve not started my production.. is it mandatory that I should serve 1 month of notice period.. or a formal resignation letter is enough pls adviae

Refer the clause of notice period in your appointment letter, generally company's do not require notice period during probation period, so I believe putting a formal resignation is enough.

If I provide a formal resignation and leave then can the employer black list me. Is it possible ?

If you provide a proper resignation letter, company won't mark you as 'Abscond'
Still there is every possibility of blacklisting you, for re-hiring in future, which means you cannot apply to same company again. However, there shouldn't be any problem with other companies.