It is observed that January 1, 2013 is a Sunday. In which year again the January 1st will fall on a Sunday ?

2019

(an ordinary yr has 1 odd yr and a leap yr has 2 odd days)

Jan 01, 2013 = Sunday

Jan 01, 2014 = Monday

Jan 01, 2015 = Tuesday

Jan 01, 2016 = Wednesday +2 odd days

Jan 01, 2017 = Friday

Jan 01, 2018 = Saturday

Jan 01, 2019 = Sunday.

Thus, 2019 is correct.