to an extent it can be said that peter hated jasper when he first met him. now personally , i don’t believe that jasper created peter, i believe that maria did ( and the peter in my head agrees with me here very strongly ). now peter hated jasper because of how he used his gift to obtain control over the newborns. now peter well knows that had jasper not done so, it would have been chaos- but at the same time he knows that had it not been for jasper, majority of those newborns could have escaped and either adapted to the change themselves, or at least had a fighting chance at surviving more than a year if another vampire didnt kill them. to be honest peter just hated the whole newborn war things in general ( but he did love to fight ).
it was only around the end of his first year that peter became aware of his gift ( if ya can call it that, which he does- but he also never tells anybody about it, he’s always just been a smart and instinctive fucker ). it was around this time that he realised that jasper was, in some ways, just as stuck as the rest of them, the difference being that he wasnt killed at the end of his first year. so about six months in, peter stopped just getting by and actually started putting effort in. this led to jasper, and by extension maria allowing him to survive past his year mark.
now there were times pete was jealous about jasper’s pathokinesis and that was when jasper could scare a newborn off before they grabbed him, whereas peter just had to fight off the attacks far more than jasper did.
peter knew jasper was struggling feeding from humans during their nomad years, so he started to leave the more drunk humans behind for jasper in the hopes that their emotions would be more muffled due to their intoxication.
peter knew jasper would be leaving charlotte and him at some point, but it still broke his heart when jasper actually left, though as soon as he knew it was going to be that cafe that jasper met alice in, he took off along with charlotte so that their emotions didnt cause jasper to change his mind or make him feel conflicted.
over the years, peter doesn’t see jasper as much as he wants to, not wanting to get in the way or intrude into a family where all he feels is unwelcome due to his dietary choices. he once tried a bunny to see how jasper could put up with it, and it made him feel sick for about a week, if not longer.
peter was all too happy to help and offer advice when jasper called him during eclipse, and peter even, because he wasnt busy, trecked all the way up to washington state to be nearby in case things went to shit and jasper needed backup. charlotte accompanied him as well and was also there for backup
despite the above point, peter was kind of pissed to be dragged into something against the volturi during breaking dawn- the only reason he rocked up being because jasper was there.
in all sense of the word, peter sees jasper as his brother, and would do pretty much anything for him.