My US contract ended in November 2018. The check for the last payment was issued on 01/02/2019. Does this payment count for 2018 tax return or for the 2019? (I hope 2018)

Your 1099-MISC (or if you received a W-2) detailing your wages for 2018 will detail what was paid to you in 2018.  Forms 1099 and W-2s are forwarded to the IRS.  Box 1 (W-2),  and Box 7 or another box #, depending on the type of income you received (1099-MISC) will show what your wages or earnings were for Year 2018.  This is what you will have to report.  The payments issued in 2019 will show up on your 2019 wages and earnings statement.  Short answer is: The paycheck is considered as taxable income in the year the paycheck is ISSUED (dated).