I only like play basketball.疑问啊

可以说 I only like playing basketball

作为副词时两种表达都是正确的

only用作副词

常位于所修饰的动词、短语或从句前，意为“只是、仅仅”。如：

At present we can only wait and see.

目前我们只好等一等看。

I only touched it.

我只不过摸了它一下。

I only regret that I have but one life to lose for my country.

我惟一遗憾的是：我仅有一次生命可以贡献给我的祖国。

He only walks to save money��he doesn”t really like walking.

他只是为了省钱而步行，并不是真正喜欢步行。

Father gave me this computer only for my birthday.

只是因为我过生日，父亲才送给我这台电脑。

My sister is in bed only because she is ill.

我姐姐在床上躺着，仅仅是因为她病了。

都可以，意思基本差不多，不过非要说的话，第一句话比较强调like，比如就不喜欢别的运动，第二句比较强调basketball,比如不喜欢play别的球类

双谓语，I only like playing basketball ＝I like playing basketball only

only 是形容词不能修饰动词
just是副词可以修饰
I just like playing basketball或
I like playing basketball only.都行

都可以，两句的意思基本差不多。
不过非要说的话，第一句话比较强调like，比如就不喜欢别的运动；