So you took what was a minor issue (a 6 month gap) and turned it into a much more serious issue, namely your trustworthiness.
Come clean, accept whatever consequences come from it, learn from it, and move on with your life.
Lying never achieves anything good or worthwhile.
Should I tell my new company about this or just leave it alone?
To be safe you should let them know. Although what you have on your resume is similar enough to your HR's title ( for any reasonable person ), it is better to give them more information that what they need right now than to have them come back to you and ask you to explain any discrepancies ...
The main problem to address here is that you lied intentionally. The 6 months are probably not a big deal, but lying is.
So you need to come clean and fess up. You need to write down and review and practice what you are going to say. This needs to be a good story and delivered well.
A big part of this story needs to be explaining why you did lie in the ...
Is there any possibility this won't end in termination?
All you can do is tell the truth to all parties involved ( your boss and the third party if you are in communication with them ) and hope for the best. If the fact that you lied and are missing 6 months of experience isn't that important to the company then you may be able to retain your job, but I ...
I think your former colleague is mistaken.
Regardless of whether you were training or on assignment, you were on that company's payroll. And that's generally the determining factor for whether you worked for another company or not.
As long as you explain it properly, you should be fine.
This may come up during employment verification, what should I say/expect?
I don't think it will come up.
But if it does, just be completely honest
You were employed at the company for a year
That year includes a paid 4-month training/probation period
Based on your contract, you feel that you were employed by that company for those 4 months
You were never ...
It sounds like your previous employer is a little bit petty. They won't be the last petty one you encounter. You're going to want to keep documentation to back up everything you put on your resume. It might be difficult to imagine why an employer would claim you didn't work for a time period based on a technicality, but just assume there's a reason they ...
I was with my previous employer for one year and within that one year they have a four month training period. [...] I was paid for those four months.
Then you were employed (and had presumably signed a contract saying so if you were paid), so this was part of your employment, and your colleague is wrong. "Whenever you're doing training we're still paying ...
Ideally, the date on offer letter from the previous company shall be ground for final decision. However, it is considered a grey area because companies/managers do treat/twist training period as per their benefits in many cases. If your appointment letter is including start of training period then there should not be any problem regardless of what your ex-...