I am looking for a way to make people detect me as evil even though I am good, or people detect me as chaotic although I am lawful. I know there are ways to completely change a character's alignment, but that is not what I am looking for. I also do not want to be protected from spells like Nondetection. Is this possible? How?
Aura Alteration spell
Aura Alteration can change your aligment aura, but will not make it show the diametrically opposed alignment (Good/Evil and Lawful/Chaotic). It has a day/level duration, though.
The Vigilante class has a class ability called Dual Identity, which says your second identity's aligment has to be within one step of your actual aligment on each axis. So a Lawful Good character has a second identity that is either Lawful Good, Lawful Neutral, Neutral or Neutral Good.
A vigilante's two alignments cannot be more than one step from each other on a single alignment axis. For example, a vigilante with a lawful neutral social identity could have a vigilante identity that is lawful good, lawful neutral, lawful evil, neutral, neutral good, or neutral evil. If a vigilante is the target of an effect that would change his alignment, it changes both of his alignments to the new alignment.
(From Lawful Neutral to Neutral Good/Evil are actually two alignment steps, but since the wording on the ability is one step on each axis, that allows two total steps so long as the steps are on different alignment axes.)
But the Faceless Enforcer archetype learns an ability called Faceless Infiltrator, which allows you to assume a third identity that has to be within one step from either of your two identities.
Which means he can make a Good character appear as Evil, or a Chaotic character appear as Lawful, but he still cannot make a Lawful Good character appear as Chaotic Evil. He could make a Lawful Neutral character appear to be Chaotic Evil if his secret identity is Neutral Evil, or appear to be Chaotic Good if his secret identity is Neutral Good.
If you are a (True) Neutral vigilante, your secret identity could be of any alignment you want. If you take the archetype and has a Chaotic Neutral secret identity, you could create a fake identity as either Chaotic Good and Chaotic Evil (from your CN identity) or Neutral Good, Neutral Evil or Lawful Neutral (from your social identity) whenever you want, expanding even more your options.
Master Spy prestige class
A 2nd level Master Spy has the ability Mask Alignment, which allows her to fake her alignment as anything she wants, even become completely diametrically opposed of her own, so a Lawful Evil Master Spy could mask her aligment as Chaotic Good.
But this only affects detecting spells. Other spells based on aligment, such as Order's Wrath still affect her normally.