I get it, it's like 「飼う」in Japanese, e.g. 「子供の時、猫を飼っていた」. But if you don't mind me asking, what does "有" mean in this sentence? Does it somehow modify "養"?
And thank you once again for great feedback!

Yep it's exactly like 飼う！:)
And I just did some research! It was my bad. The structure "有+verb" is commonly used mostly by people in Taiwan and Hong Kong. In China you'd use "過" or "了" to show the past tense, so you'd say "我小時候養過一隻貓" if your target audience is Chinese (though I think they'd understand you as well if you say "有養").
In case you want to know, we use "有+verb" (so 有 is kind of like an auxiliary verb in this case) to express an action that is completed. It would give the verb more emphasis, and also sound more natural (at least this is the case around here!)
Examples:
我昨天有寫作業。(I did my homework yesterday. And it "amplifies" the verb in the sense that, it's like you want to express, "I did my homework yesterday. I'm a good student!"
我今天有吃晚飯。 (I have eaten dinner today. Same as the above example, it's like saying "I have had dinner today so I'm not hungry now.")
It can also used to describe present situations, or like hobbies.
Examples:
我有養貓。（猫を飼っている）
我有戴眼鏡？（メガネをかけているの）
我有看書。（本を読んでいる, as in you do it as a hobby and do it regularly.)
But note that it's not the same as ている, for habitual actions like 毎日車で会社に行っている you'd still say "我每天都坐車上班"). It's a bit complicated I know! But you'd start getting used to it and get a hang of when to use which structure as you learn! :)
Again, sorry for confusing you with this structure! I didn't think about it at the time I corrected it, since it just came very naturally and it is what I read and write everyday haha. x

Sorry I was a bit sleepy and had a few typos hahahh, please let me know if you're confused about anything :)