Take exotic weapon: bastard sword. Or take a level of cleric.
Unless you're GM will house rule it, that's it, unless I missed something somewhere.
If anyone should be allowed to wield the favored weapon of a Deity it should be the melee-oriented Paladin. As a DM I do allow it.
It's never come up for an Inquisitor, but I would probably agree to it as well.
here my Paladins favorite weapon. Its even named after us Paladins. http://en.wikipedia.org/wiki/M109_Paladin
Do I have to spend an exotic feat to use it?
Yes you do have to spend the feat. Paladins are already proficient in all marital weapons, all armor and all shields except tower shields. The cleric and inquisitor on the other hand have a very poor selection of weapons and armor available to them. No one says you can't use your deities favored weapon you just need to spend a feat if it is an exotic weapon.
Customizing your character is why you are getting the feats.
Mysterious stranger makes a good point. Perhaps it'd make sense for the Paladin to give up some/all martial weapon training, focusing instead on his favored weapon. Certainly not RAW though.
Inquisitors do get proficiency in their favored weapon.
If anyone should be allowed to wield the favored weapon of a Deity it should be the melee-oriented Paladin. As a DM I do allow it.
It's never come up for an Inquisitor, but I would probably agree to it as well.
So because I am a paladin that worships a specific deity I get a in game advantage over all other paladins? That does not seem right. It is all well and good to say a paladin of Ragatheil should be able to use a bastard sword one handed, but what about a paladin of Sarenrae, or Iomedae? Are you going to give them weapon focus with their deities weapon for free?
All characters get a feat at first level use your feat for exotic weapon proficiency bastard sword if you really want to use the bastard sword with a shield. If you do decided to give the feat away for free I suggest taking away the proficiency with all martial weapons and downgrading it to simple weapons.
Character concept is all well and good, but it should not give a in game advantage over someone with a different concept.
This is your campaign so you are free to do what you want. This is just my two cents worth.
It still sets a bad precedence. What if the deity uses a more powerful weapon?
I'd be more inclined to give oracles the favored weapon proficiency. But I've even denied that to a player who asked.
And paladins really don't need even more stuff, they are strong enough.
here my Paladins favorite weapon. Its even named after us Paladins. http://en.wikipedia.org/wiki/M109_Paladin
Do I have to spend an exotic feat to use it?
Not sure, but if the feat is needed, I have it. Actually I think it is just a Martial Weapon.