First off, your object, this is how you set this up, an example:
Book.h
#import <Foundation/Foundation.h>
@interface Book : NSObject
@property (strong, nonatomic)NSString *bookID;
@property (strong, nonatomic)NSString *publishingYear;
@property (strong, nonatomic)NSString *author;
@property (strong, nonatomic)NSString *printHouse;
@property (strong, nonatomic)NSString *title;
@property (strong, nonatomic)NSString *ISBN;
-(id)initWithBookObjectId:(NSString *)bookID
           publishingYear:(NSString *)publishingYear
                   author:(NSString *)author
               printHouse:(NSString *)printHouse
                    title:(NSString *)title
                     ISBN:(NSString *)ISBN;
- (id)initWithDictionary:(PFObject *)dic;
@end
Book.m
#import "Book.h"
#define NSHNullCheck(object) ([object isKindOfClass:[NSNull class]] ? nil : object)
@implementation Book
{
    NSDictionary * descriptionDict;
}
-(id)initWithBookObjectId:(NSString *)bookID
           publishingYear:(NSString *)publishingYear
                   author:(NSString *)author
               printHouse:(NSString *)printHouse
                    title:(NSString *)title
                     ISBN:(NSString *)ISBN;
{
    self = [super init];
    if (self) {
        _bookID = bookID;
        _publishingYear = publishingYear;
        _author = author;
        _printHouse = printHouse;
        _title = title;
        _ISBN = ISBN;}
    return self;
}
- (id)initWithDictionary:(PFObject *)dic
{
    self = [self initWithBookObjectId:dic.objectId
                       publishingYear:NSHNullCheck([dic  valueForKey:@"publishingYear"])
                               author:NSHNullCheck([dic  valueForKey:@"author"])
                           printHouse:NSHNullCheck([dic  valueForKey:@"printHouse"])
                                title:NSHNullCheck([dic  valueForKey:@"title"])
                                 ISBN:NSHNullCheck([dic  valueForKey:@"ISBN"])];
    descriptionDict = @{ @"sessionObjectId":_bookID,
                         @"teacherAge":_publishingYear,
                         @"teacherEmail":_author,
                         @"teacherFacebookuniquekey":_printHouse,
                         @"teacherFirstname":_title,
                         @"teacherGender":_ISBN};
    return self;
}
- (id)init
{
    self = [self initWithBookObjectId:nil
                       publishingYear:nil
                               author:nil
                           printHouse:nil
                                title:nil
                                ISBN:nil];
    return self;
}
- (NSString *)description
{
    return descriptionDict.description;
}
@end
Storing data in object Model:
books is an array that holds your "book objects"
The following snippet of code goes in whereever you pull your data from the network with a query from Parse.
for (PFObject *object in objects) { //"objects" here is the NSArrray returned from the parse query!
    Book *book = [[Book alloc] initWithBookObjectId:object.objectId];
    book.publishingYear = object[@"publishingYear"];
    book.author = object[@"author"];
    book.printHouse = object[@"printHouse"];
    book.title = object[@"title"];
    book.ISBN = object[@"isbn"];
    [self.books addObject:book];
}
if ([self.searchTerm isEqualToString:@""]) {
    self.filteredBooksArray = self.books;
} else {
    NSPredicate *predicate = [NSPredicate predicateWithFormat:@"SELF.title contains[c] %@",self.searchTerm];
    self.filteredBooksArray = [NSMutableArray arrayWithArray:[self.books filteredArrayUsingPredicate:predicate]];
}
[self.booksTable reloadData];
So, this is how you do search with PFObjects, you first need to extract the data, save this data inside an NSObject subclass (a data object model) and then use regex predicates as you would on any object model with a search function in IOS. 
There's this method:
PFQuery *query = [PFQuery queryWithClassName:@"Post"]
[query whereKey:@"hashtags" containsAllObjectsInArray:@[@"#parse", @"#ftw"]];
NSArray *parseFTWPosts = [query findObjects];
and then this method:
/ Using PFQuery
 [query whereKey:@"playerName" notEqualTo:@"Michael Yabuti"];
 [query whereKey:@"playerAge" greaterThan:@18];
 // Using NSPredicate
 NSPredicate *predicate = [NSPredicate predicateWithFormat: @"playerName != 'Michael Yabuti' AND playerAge > 18"];
 PFQuery *query = [PFQuery queryWithClassName:@"GameScore" predicate:predicate];
and then this snippet:
Specifying Constraints with NSPredicate
To get the most out of PFQuery we recommend using its methods listed below to add constraints. However, if you prefer using NSPredicate, a subset of the constraints can be specified by providing an NSPredicate when creating your PFQuery.
NSPredicate *predicate = [NSPredicate predicateWithFormat:@"playerName = 'Dan Stemkosk'"];
PFQuery *query = [PFQuery queryWithClassName:@"GameScore" predicate:predicate];
let predicate = NSPredicate(format: "playerName = 'Dan Stemkosk'")
var query = PFQuery(className: "GameScore", predicate: predicate)
These features are supported:
    Simple comparisons such as =, !=, <, >, <=, >=, and BETWEEN with a key and a constant.
    Containment predicates, such as x IN {1, 2, 3}.
    Key-existence predicates, such as x IN SELF.
    BEGINSWITH expressions.
    Compound predicates with AND, OR, and NOT.
    Sub-queries with "key IN %@", subquery.
The following types of predicates are not supported:
    Aggregate operations, such as ANY, SOME, ALL, or NONE.
    Regular expressions, such as LIKE, MATCHES, CONTAINS, or ENDSWITH.
    Predicates comparing one key to another.
    Complex predicates with many ORed clauses.
and more here:
https://github.com/ParsePlatform/Docs/blob/master/en/ios/queries.mdown