Which progeny (son) is eiligble  for offering

 with compassion (to donate, for adoption) ?

In the Adikavi Valmiki Ramayanam, it is said,

 the son can be offered the religious piety to others.

Means the son can be donated to some

one who wants to accept him as alms.

But, in that sacred script of epic, it is said,

 the eldest son is the first progeny.

He is the divine progeny.

He is deserved for all the religious observances

and customs to follow in the family in future

when his father leaves the mortal body.

 So the eldest is not  eligble for the

offering with compassion to be donated others.

The youngest son is the  pampered and caress progeny.

 He is known as  Jnana Santanam (progeny for wisdom).

So the youngest also  is not  eligble for

 offering with compassion to donate.

The  son who is middle of the progeny is

 the symbol for the lustful desire.

Means he is known as Kaama Santanam,

the progeny of passionate.

Therefore this son is deserved tobe  for adoption.