Guessing you are asking about Merit Scholarship? 1350 is top 5-6% of all HS testers in U.S., likely GPA/Ranking and similar EC, you are competing with 100,000 students.
I would look at bottom $ (Average Net Price) not the scholarship.
scenario: two local colleges, one gives my D 80K for 4 years and one doesn’t. When you calculate Total ANP, we are paying 40K more with scholarship.
Did he apply to schools that would give a lot of merit for those stats? If not, and you need merit to afford college, then look for schools that will still award merit…maybe UToledo, miss state Univ, UAH, UAB, etc.
Others can chime in with some more ideas.
The private awards that you’re looking at are likely for one year, freshman year only… 
What is his major and career goal and what do you need his net cost to be?
Try Auburn, Alabama, SUU, and Wyoming. Those schools are the most generous for out of state students as far as I know. Also try some private schools like SMU, and TCU. You’ll be surprised how much need based aid they can offer. Just log your financial aid info into the net price calculator.
Looking for NOT school specific.
Most outside scholarships will be local ones. He will be competing with others in the area so it can be a challenge to get them. Other outside scholarships are very competitive and very time consuming. They are also fairly small in comparison to the overall COA. As others have mentioned the most scholarship money will come from the schools themselves. On the whole the higher ranked your student is to the incoming class the better. Looking at directionals or mid tier publics and privates will garner your student a better chance for scholarships than flagships or selective privates. Your child has good stats and should be able to find schools that would offer him/her scholarship money. You may need to look at less selective universities. The good news is they can still be very good universities.
Definitely look locally - the GC’s office, google your city or county name +scholarships. My kids got several (one was a 4 year if she kept a certain gpa), and all were sponsored by our town, our county or the larger city nearby.
We’re lucky in that our county has a common app of sorts run by the county foundation that is a clearinghouse for lots of local scholarships. Students can plug in and see what they qualify for then input their basic info once, with some essay or financial supplements for certain ones.
We’re already in the University. Just looking to fill a $3k gap. Applied for Good Citizen, and trying for one thru work. Just wondering about any others.
My daughter worked for 3 years setting up a list of outside scholarships to apply for. She had grades similar to your child, with excellent volunteer (raised 3 Seeing Eye puppies, among others) and leadership. Great recommendations, engaging essays. She is not a minority nor are we poor.
She ultimately brought in 8,000, and has since added to that total by winning additional scholarships at the departmental level in college.
That was with all that prep work and hitting every deadline. It is not an easy way to pay for college. We did feel it was great return on investment - she also learned a lot about project and time management - so win win 
Still it was no slam dunk way to pay all college expenses, and I still want to laugh every time I hear a clueless person say “There are so many scholarships that are so easy to get!”
From her experience I can tell you most of the scholarship applications are closed by now. In our area local ones were just opening and applications due by early March.
Are you trying to fill a 3K gap times 4 years (12K total) ?
Well maybe $3k Times 2 years. Yeah it seems local ones are just now opening. They all wanted first semester transcripts, which are available starting 2/12!
Oh yeah - apply to Arizona State . . . go devils!
LOL, some of you aren’t reading. He’s already been accepted to his university. Looking for outside scholarships. I guess we’ll focus on local ones.
Local civic groups are worth a try… a couple $1,000 or $1,500 scholarships would fill your gap. Down side is that these are usually one-time awards. I used to read scholarship applications for a local group… sometimes candidates with high grades and scores made the cut, but sometimes it was the kids with work experience or meaningful community service or leadership.
Does he have a summer job and on campus part time job?
Did he already take his student loan?
He starts college in the fall. We are planning on the $3500 Loan and a 10-15 hour a week work study.
Check the websites of surrounding high schools (public and private) - most of them will likely have a college and career section which will list current and upcoming scholarships. We found out about additional local scholarships that way. Be careful of competitions at the national level that aren’t well know … they are really just data gatherers posing as scholarship competitions. Again, just my opinion.
If all else fails, he can take $2000 additional Direct Loan but it won’t be subsidized.
Did he receive work study as part of his financial aid award?
Also, he should be able to earn at least $1000 working this summer…and that will help for expenses when college starts. If he gets a work study job, it could be weeks before he sees his first earnings after the fall term starts.
Your reply above made it sound like he was a current college student.
There might still be time to apply to other more affordable schools if he is a high school senior.
But yes, he should try and earn money this summer, and do work study during the semester (but that money is earned as he works, so not available when the first bill is due). And he can borrow up to $5,500 a year in student loans.
He’s already applied to colleges and been accepted to several. All are similar price - in state public.
He does have $1k in the bank and should earn $2k this summer but was thinking he’d use that for incidentals. Trying to avoid taking out unsubsidized student loans. Our PTSA has scholarships but there’s only 7 of them so I was thinking they’d be hard to get since he’s not top 10%.
We paid the interest annually on the unsubsidzed portion of the loans while,the kids were in college. It was NOT expensive to do so…and better than having the interest compound in terms of eventual payments.
So…we just subsidized those loans!