A sorcerer may focus their inner magic more narrowly, losing access to the wider availability of spells in exchange for other benefits. Each purist archetype loses access to one or more schools of magic, chosen at 1st level. The sorcerer treats spells of this school as if they were not on her class spell list. She still gains bloodline spells of this school, if any, normally. This choice cannot be changed.
Battle Purist
The sorcerer spends more time training in martial studies than exploring the breadth of magic.
Benefit: The sorcerer's BAB becomes equal to that of a cleric of her level and her hit die becomes a d8. Additionally, she loses one spell per day of each level of spell she can cast. This replaces one school of magic.
Bloodspell Purist
The sorcerer focuses her efforts in awakening the mystic powers of her ancestry earlier.
Benefit: The sorcerer treats her class level as 2 levels higher for the purpose of learning bloodline spells. At each level where she knows a spell higher than her highest spell slot, her spells per day of the spell level equal to the highest level spell she knows becomes 0 instead of -. She may gain bonus spells per day of this level for a high charisma score. This replaces one school of magic.
Devoted Purist
The sorcerer's religious inclinations take up a significant portion of her arcane delving.
Benefit: Choose one cleric domain. This domain may not be of an alignment opposite to any component of the sorcerer's alignment. The sorcerer adds the spells granted by this domain to her class spell list and may learn them as arcane spells. This replaces one school of magic.
Skilled Purist
The sorcerer's narrower focus permits more time to study mundane pursuits.
Benefit: The sorcerer gains an additional 2 skill ranks per level. This replaces one school of magic.
Feel free to comment and suggest your own along the lines of this archetype mechanic.
And some more!
Charge Purist
The sorcerer develops an innate connection with magic items in place of a breadth of magical study.
Benefit: When using a potion, scroll or wand, the sorcerer may expend a spell slot of any level to increase the caster level of the item. The caster level is increased a number of levels equal to the spell level of the expended spell slot, to a maximum of the sorcerer's caster level. This replaces two schools of magic.
Spellfont Purist
The sorcerer devotes more energy to casting more spells than learning a variety.
Benefit: The sorcerer can cast an additional spell per day of each level of spell she is able to cast. This replaces one school of magic.
Discovery Purist
The sorcerer's arcane study extends to more wizardly affairs.
Benefit: When selecting a bloodline feat, the sorcerer may choose an arcane discovery as if she were a wizard of her sorcerer level instead. This replaces one school of magic.
This 'purist' mechanic is horrible. It's one thing to sacrifice spells per day or even spells know, but to specifically make a player choose to forever ban an entire school of magic is pointless, and no experienced player would ever take that option. The schools of magic are NOT perfectly balanced in their abilities, how useful their spells are, or even how many spells are in each school.
Not even the Wizard has to completely bar access to any spell schools anymore. If you are going to alter the Sorcerer class, you should do so by altering the Bloodline; nothing more, nothing less. Something like this is a little more appropriate:
Battle in Blood
The drums of war beat in perfect rhythm in the sorcerer's heart, the call to arms all but completely irresistible to them.
Benefit: The sorcerer's base attack bonus becomes equal to 2/3 of their hit dice, as a cleric or a rogue of their level and their hit die is increased from d6 to d8.
Drawback: The sorcerer does not gain the bonus spells associated with their bloodline and the number of spells per day of each spell level that the sorcerer can cast is reduced by 1. If the sorcerer's daily allotment of spells for a level would be decreased to 0, they only can cast as many spells per day as allowed by their Charisma modifier.
I like the "remove school from spell list" mechanic, and it's something the wizard should have had. However, the benefits seem too low on paper for such a large penalty. On the other hand, sorcerers don't know that many spells anyway so ignoring a school may not be that big of a deal. It may also depend on how high level you think you'll reach.
It's certainly not a power creep, which is good, and the abilities are interesting, which is good. They may be a little too weak, but I'm not sure about that.
More specifically:
Battle Purist - this one seems fine and I could see it used, especially if you use touch attacks a lot.
Bloodspell Purist - Don't know how good this is, but more spells per day is always powerful. Very nice if you want to make a mystic theurge. So circumstantially nice, which is as it should be.
Devoted Purist - Too weak IMO, since you have to learn them specifically and cleric domain spells aren't usually that powerful and highly circumstantial. Might be worth considering granting knowledge of a spell or two for free.
Skilled Purist - Too weak. Skill points aren't worth that much. +4 skill points per level, or grant two class skills of choice, and it's probably fine.
Charge Purist - Think the cost is too high, especially since those two lost schools mean he can use fewer wands and scrolls. One school is probably enough.
Spellfont Purist - This is the only one that I think is really good. Might be a bit too good, but I'm not sure.
Discovery Purist - Too weak. Few of the discoveries are good, and the one that is REALLY nice (fast study) won't work for a sorcerer. At least give a free discovery too. Or combine this one with the Skilled purist.
They are deliberately erring on the weak side, yes.
On the other hand, I have played many sorcerers that never even bothered with spells of one or two schools, just because I wasn't interested in them. In such cases, taking one of the above would be no loss at all.
You can also ignore some of the penalty by taking a bloodline that has many bloodline spells of the school you are removing.