What I have found:
"The words “fertile” and “sterile” refer to the trees, where fertile trees stands for ones with branchlets which are the clusters of short leafless branches for fruits bearing, while sterile trees
do not have such organs. Individual fertility is assessed, easily recognized from the existence of branchlets which are specialized branches bearing clusters of fruits (Fig. 4)."
So, it would appear that the sycamore fig is the kind most likely referred to in the Bible rather than ficus carica, the more familiar common fig. It also appears such fig trees do bear fruit on short leafless branchlets which are specialized branches only for fruiting, but this is not the same as saying that the tree produces fruit before it produces leaves. There is no indication in any of these descriptions of the biology of the fig that the fruit comes at a time when the tree has no leaves at all, which would seem a fairly important characteristic.
No discussion of types of figs, however, gets around the statement in Mark that “it was not the season for figs.” So, it partly depends on whether you are using the version in Matthew or in Mark, which have some fairly significant differences.
Mark 11: 12-14, 20-25
12The next day as they were leaving Bethany, Jesus was hungry. 13Seeing in the distance a fig tree in leaf, he went to find out if it had any fruit. When he reached it, he found nothing but leaves, because it was not the season for figs. 14Then he said to the tree, “May no one ever eat fruit from you again.” And his disciples heard him say it.
20In the morning, as they went along, they saw the fig tree withered from the roots. 21Peter remembered and said to Jesus, “Rabbi, look! The fig tree you cursed has withered!“
22"Have[f] faith in God,” Jesus answered. 23"I tell you the truth, if anyone says to this mountain, ‘Go, throw yourself into the sea,’ and does not doubt in his heart but believes that what he says will happen, it will be done for him. 24Therefore I tell you, whatever you ask for in prayer, believe that you have received it, and it will be yours. 25And when you stand praying, if you hold anything against anyone, forgive him, so that your Father in heaven may forgive you your sins.”[g]
Matthew 21: 18-22
18Early in the morning, as he was on his way back to the city, he was hungry. 19Seeing a fig tree by the road, he went up to it but found nothing on it except leaves. Then he said to it, “May you never bear fruit again!” Immediately the tree withered.
20When the disciples saw this, they were amazed. “How did the fig tree wither so quickly?” they asked.
21Jesus replied, “I tell you the truth, if you have faith and do not doubt, not only can you do what was done to the fig tree, but also you can say to this mountain, ‘Go, throw yourself into the sea,’ and it will be done. 22If you believe, you will receive whatever you ask for in prayer.”