You wouldn't usually receive a second W-2 when you change from full-time to part-time with the same company. If it shows that you didn't have enough withholding throughout the term of your employment, it is likely because your Form W-4 wasn't updated to change your withholding.
Unfortunately, there isn't anything that you can do about it for 2019, but you should fill out a new form for 2020 and submit it to your employer as soon as you can. You can find that form here: Form W-4 2020.
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