It's not a baby though you hold in the arms close to your bosom.
It's not an Indian man though it has long beard.
It's not a monkey though its tail is bent.
It's not a bird though it has beautiful voice.
What am I?
Are you talking about
A beard guitar?
It's not a baby though you hold in the arms close to your bosom.
You hold it close to your bosom while playing it.
It's not an Indian man though it has long beard.
Does the name of the instrument answers this clue?
It's not a monkey though its tail is bent.
The end of the guitar is a bit bent.
It's not a bird though it has beautiful voice.
Who doesn't like to listen to a beautiful guitar being played?
I think answer is
Pet Dog. Affenpinscher is one of example
It's not a baby though you hold in the arms close to your bosom.
We can hold pet in the arms
It's not an Indian man though it has long beard.
Some pet dog has long beard
It's not a monkey though its tail is bent.
All pet dog has tail is bent
It's not a bird though it has beautiful voice.
Some pet dog has beautiful voice like Pug Dog.
Inspired by Paul's answer, I'll stick with the music theme.
a saxophone
It's not a baby though you hold in the arms close to your bosom.
you need to hold it close to play it
It's not an Indian man though it has long beard.
when you play it, it's like you have a long golden beard
It's not a monkey though its tail is bent.
the end of a saxophone is usually bent
It's not a bird though it has beautiful voice.
it's a pretty nice music instrument (but my Trombone is better)