Judging from fruit, stem and leaf characters, this is most likely Candelabra Cholla (Cylindropuntia imbricata ssp. imbricata) native to Mexico and the southern-central U.S., but other similar species should also be considered including C. imbricata ssp. spinosior and C. thurberi ssp. versicolor.
Overall, a number of species of opuntioid cacti produce green, fleshy leaves on young growth. These leaves usually fall off as the stem matures. Such leaves are longest and most persistent on some species of Austrocylindropuntia, such as A. cylindrica, A. subulata, and A. vestita.