So I set up a partition on my HDD /dev/sdb of 100 GB for the operating system. I set up root, home, and swap area all within that partitioning of my 2Tb HDD. I restart my system and find Linux Ubuntu has also gone ahead, took control of my /dev/sda WDS250G2B0A 250GB SSD, and formatted the whole thing. I had entire projects for applications that were complicated and almost finished. I don't have the money to spend on giant back ups. I figured a partition would be safe enough. Then Linux did this to me. I wanted to know if there are HARD Recovery specialists, like the people who recover formatted disks. I know it would probably be extremely expensive. But I just lost most of my livelihood and am shaking.
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If the SSD has been formatted with ext4 or swap, then most likely, the data is gone forever. This is because SSDs have a feature called TRIM/discard, and ext4 (mke2fs) as well as swap make use of it by default, without asking you for confirmation.
Once trimmed, the SSD won't waste much time to actually erase cells for good, as that is how it gains performance for future write requests. Not even a data recovery lab will be able to restore anything.
SSDs are capable of throwing away all data in an eyeblink, it's a feature that Linux unfortunately makes extensive use of. See also my TRIM related answer here.
If a data recovery company is an option for you, pull the plug and send it in. Most likely they'll happily recover your fresh Linux install for you...
Otherwise you can run
photorec on it, or even a simple
strings /dev/ssd | grep MyLostStuff (assuming the data wasn't encrypted), and see what, if anything, would be found of your old files.
If you ever copied any of your data to any other storage device, you'd likely have better chances to recover it from there.