I worked for the State of Alaska Department of Corrections as an inmate during the last few weeks of December 2018. Do I need to obtain documentation for wages acquired during that time to report on m

No, you only report wages for which were you paid in 2018 on the 2018 return.  If you had received payment in 2018, you would have received any documentation you needed for those wages

I did receive wages for the few weeks that I worked in December 2018. Do I still need to report wages and earnings for which were paid for hours worked in Decmber 2018 on January 4th, 2019?