BABA agac gibidir meyvesi olmasada gölgesi yeter... ama yokluğuda güneşsiz bir yaz mevsimi gibidir, içini karartır

 Baba ağaç gibidir

 Father is like a tree

 meyvesi olmasa da gölgesi yeter..

 His shadow is good enough even if he has no fruits...

 ama yokluğu da güneşsiz meyve gibidir,

 but his absence is also like a fruit with no sun. (a fruit that doesn´t see sunlight )

However, there is "bir yaz mevsimi", not "meyve" in original sentence. Could it be translated like this? (learner´s try)

ama yokluğu da güneşsiz bir yaz mevsimi gibidir

But his absence is also like a summer (season) with no sun

içini karartır (I think it is iç-in-i ?)

It darkens your soul.

correct.

 I would interpret yokluğu not relating to him (baba) but to it (meyve).

But their absence is like summer without the sun

It darkens your soul

Just as a tree should have fruit, and summer should bring the sun, it is sad for someone not to have any children.