It's a great coin to be sure, but from that image, I can't tell if the green on the reverse is mineral deposit, or if the coin was painted to cover bad surfaces. In either case, I would leave it alone. If you removed it, you might not like the result, whereas the coin looks perfectly nice as it is.
Hadrian Sestertius Roma 118 AD Fortuna Reference. RIC 551a; Banti 414 Obv. IMP CAESAR TRAIANVS HADRIANVS AVG Bust of Hadrian, laureate, draped on left shoulder, right Rev. PONT MAX TR POT COS II S C FORT RED Fortuna, draped, seated left on low seat, holding rudder on ground in right hand and cornucopiae in left. 26.04 gr 33 mm Vcoins
Hadrian Denarius Roma 125-128 AD Roma Reference. Strack 121; RIC 77; C. 1104 Obv. IMP CAESAR TRAIAN HADRIANVS AVG. Laureate, cuirassed and draped bust right. with very unusual Bust drapery Rev. P M TR P COS III. Roma seated left on cuirass, holding spear and Victory, shield with quiver behind. 3.26 gr 19 mm h7
Hadrian Sestertius Roma 134-38 AD Tellus Reference. Scarce Strack 698; RIC 791f; C. 1432; Banti 758 (same die) Obv. HADRIANVS AVG COS III P P Bust of Hadrian, laureate, draped, right, wearing paludamentum. Rev. TELLVS STABIL in ex. S C Tellus, draped, reclining left on ground, resting right hand on globe and left on basket of fruit, and holding vine-branch in left hand. 25.8 gr mm h