You are no longer employee of the company
2) you are at liberty to work with US company after you have resigned from your old organisation
Can I get detail about my these queries below: 1. Once my company hired me via interview, they never gave me joining letter but communication was verbal to join the company even the salary they gave me was directly in my bank account (online), there were no mentioning of clause by that company to me, that company never signed any contract/agreement/terms with me, but later I resigned from that company by sending the employer resignation email, and that employer didn't send me relieving letter, so I was no longer employee of that company since the time of my resignation? 2. Later after 5 months when I resigned from my old company, I applied in USA based company, as that company details were available from internet by Google and that USA based company also does job postings in internet and other job websites, and that same USA company was also working with my old company, as I mentioned in the point 1 there were no contract/agreement/terms signed by me with company, so I can work with that USA company without any issue?
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You are no longer employee of the company
2) you are at liberty to work with US company after you have resigned from your old organisation
You were an employee of previous employer but there was no offer letter, no terms were agreed, no cluse governing resignation or termination was mentioned. Your employment was at will that is, the employer can fire you any time and you can resign any time at your will. You have submitted a resignation and therefore successfully terminated the employment. You are a free bird now. You can joint any employment, your ex has no right to take any objections.
As you do not have any agreement with the previous employer regarding the terms and conditions of employment and that your resignation was already tendered for which the previous company neither objected nor respond to it, hence you can be considered to have resigned your job properly and in a legally valid manner.
Therefore there is no necessity to hesitate to join the new job of USA based company.
There is no bar or restriction to join the new company.
You can work with the USA company as you've not executed any non-compete with your previous employer. In absence of it, you can freely join any company now.