Parashurama killed many kshatriyas 21 times. The confusion is between Krita yuga and Treta yuga.
In which yuga did this Kshetriya massacre happen?
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Chapter 47 of Matsya Purana states that in the 19th Treta Yuga , Lord Vishnu incarnated on earth as Parshurama. And Ramayana has taken place in 24th Treta Yuga. And each Mahayug has 4 yugs. So total yugs between 19th Treta Yug and 24th Treta Yug (both inclusive) would be 21. Hence the reference to 21 times. Otherwise the entire concept of getting rid of kshatriyas 21 times does not make sense. It cannot be that all kshatriya dynasties were moving in parallel.
"In the interval between the Treta and Dwapara Yugas, Rama (the son of Jamadagni) great among all who have borne arms, urged by impatience of wrongs, repeatedly smote the noble race of Kshatriyas. And when that fiery meteor, by his own valour, annihilated the entire tribe of the Kshatriyas, he formed at Samanta-panchaka five lakes of blood."
The mahabharata describes that during the interval of treta yuga and dwapara yuga, Parashurama slew the kshatriyas and how he formed the samanta-panchaka where the battle between the kauravas and pandavas were later fought during the intervals of dwapara yuga and kali yuga.
"In the interval between the Dwapara and the Kali Yugas there happened at Samanta-panchaka the encounter between the armies of the Kauravas and the Pandavas. "
Parshurama started massacre of kshatriyas after death of his father in hands of Kartavyavir Arjuna.
10) When Râma one day with his brothers was away from the âs'rama in the forest, they, seeking revenge, took the opportunity to approach their residence. (11) Finding the muni sitting at the fireplace fully absorbed in contemplating the Supreme One Praised in the Verses, they, determined to do evil, killed him. (12) Being most cruel towards the poor and unprotected mother of Râma who begged for the life of her husband, they, those 'kshatriya' brothers, violently cut his head off and took it away. (13) Renukâ, the chaste wife down in tears grieving, stroke her body with her hands and cried loudly: 'Oh Râma, oh Râma, my dear son!' (14) Hearing the sound of that most sad cry 'Oh Râma', they [Râma and his brothers] from far away, hastened back to the âs'rama where they saw that their father had been murdered. (15) Bewildered by the shock, they all lamented and angrily, depressed, sad and indignified cried: 'Oh father, oh saint, you who are such an example of dharma have now departed for heaven and left us behind!' (16) Thus bewailing their father, Paras'urâma entrusted the body to his brothers and personally took up the ax, determined to put an end to the kshatriyas. (17) Râma went to Mâhishmatî, [the capital] that was bereft of all glory because a brahmin had been killed. There he in the middle of the town made a great pile of the heads he severed from their bodies. (18-19) Their blood formed a terrible river that brought fear to all the rulers who defied the brahminical culture. Because the kshatriyas, the royal class, had killed his father, he acted to their detriment and twenty-one times over wiped them off the earth. He as a master of war thus at Samanta-pañcaka created nine lakes filled with blood instead of water.
Parshuram took revenge of his father's dead by killing sinfully kshatriyas. It means that massacre of kshatriyas started after death of Kartavyavir Arjuna. Kartavyavir Arjuna once captured Ravan.
(20) When he one day surrounded by beautiful women enjoyed the water of the Revâ [the Narmadâ], he, overly proud of being decorated with the garland of victory, with his arms stopped the flow of the river. (21) The conceited hero called Ten-head [Râvana] could not bear that influence because the water, which moved upstream from his actions, had inundated his camp. (22) Râvana, who insulted him [the king] in the presence of the women, was without much difficulty arrested by him, held in custody in [their capital] Mâhishmatî and then released again as if it concerned a monkey.
It means that incident of kshatriyas massacre by Parshuram, Ravan and Kartavyavir Arjuna were of same yuga.
In Valmiki Ramayana, it was not mentioned as to how many times Parasurama extirpated kshatriyas. The word that was used was "anekashaH - many times".
वधमप्रतिरूपं तु पितु श्शृत्वा सुदारुणम्।
पृथिवीं चाखिलां प्राप्य काश्यपाय महात्मने ।
यज्ञस्यान्ते तदा राम दक्षिणां पुण्यकर्मणे ।
"O Rama Having heard the slaying of my father incomparable in extreme ruthlessness, I decimated the Kshatriya race again and again out of fury as they were born and reborn. I conquered the entire earth. At the conclusion of the sacrifice I conferred it on the great soul Kasyapa of meritorious acts. Gifted with ascetic energy I have (now) made the Mahendra mountain my abode."
However, in Mahabharata it was mentioned that Parasurama eliminated Kshatriyas for 21 times.
'In olden days, Rama, the son of Jamadagni, in anger at the death of his father, slew with his battle axe the king of the Haihayas. And Rama, by cutting off the thousand arms of Arjuna (the Haihaya king), achieved a most difficult feat in the world. Not content with this, he set out on his chariot for the conquest of the world, and taking up his bow he cast around his mighty weapons to exterminate the Kshatriyas. And the illustrious scion of Bhrigu's race, by means of his swift arrows annihilated the Kshatriya tribe one and twenty times.
So if the OP is interested in the number, ie., 21 times, then it can be inferred that massacre of Kshatriyas occurred in Dwapara Yuga or in Mahabharata times.