Tom Armstrong

They were both signed incorrectly, unfortunately. Thank you for the clarification, I'll be much more careful this go around. 

What you paid was a filing fee.  You filed.  What you filed was denied.  You file again with a new filing fee.
 
You can reprint the form from the same PDF file and sign it yourself in the right place, but you will have to refile the whole package.  That's the only "fix".  It's been denied because of your error.  This error will cost you time and money.  Many mistakes are expensive.  My additional advice though is to make sure you understand the whole process, and become an A-Student of all the I-130 instructions (a separate document from the form itself) and look everything over again after you're sure you understand.  We're here to help with remaining questions.
 
Perhaps you thought the I-130 was  a visa application. It's not.  When YOUR (you the petitioner) petition is approved in her behalf, she will be invited to apply for a visa, and you will provide an affidavit of support.  More documents and supporting documents will be provided at that stage.

Well it may be because it was signed by the beneficiary as the preparer. Not a simple signed in the wrong spot or forgot to sign. On ours we neglected to sign the portion for my step daughter, they just rejected it without cashing the check. We signed it properly and resubmitted. Thankfully we only lost about 20 days. Wife was just approved and sent to NVC but now we are waiting for step daughters to catch up. 
 
After reading the section it appears that preparer is probably the one spot if signed by mistake cannot have a exception or correction for good cause.
 
Chapter 5 - Interpreters and Preparers
  If an interpreter assists the benefit requestor in reading the instructions and questions on a benefit request, the interpreter must provide his or her contact information, sign, and date the benefit request in the section indicated.
If a preparer assists the benefit requestor in completing his or her benefit request, the preparer and any other person who assisted in completing the benefit request must provide their contact information, sign, and date the benefit request in the section indicated.
If the person who helped interpret or prepare the benefit request is an attorney or accredited representative, he or she must determine if the level of involvement and rules of professional responsibility require him or her to submit a signed and completed Notice of Entry of Appearance as Attorney or Accredited Representative (Form G-28) with the benefit request. If the person intends to represent the benefit requestor before USCIS, he or she must submit a completed Form G-28. The attorney or accredited representative of the benefit requestor cannot serve as an interpreter during the interview.[1] 
Footnote
[^ 1] Officers cannot make exceptions for good cause.

It's interesting that it was denied and not rejected, as the USCIS Manual Volume 1 Chapter 2 says that signature errors usually result in a rejection ("USCIS rejects any benefit request with an improper signature and returns it to the requestor"). Usually a denial is the result of an adjudication (see USCIS Volume 1 Chapter 9 -- "If, after evaluating all evidence submitted (including in response to a Request for Evidence (RFE) or Notice of Intent to Deny (NOID), if applicable), the officer determines the requestor is ineligible for the benefit sought, the officer denies the benefit request."). As others have mentioned, I would refile.
 
Filling immigration forms is one area that requires the utmost care to ensure accuracy. Mistakes just increase your exposure (and need to be corrected when noticed!) Just save yourself future headaches by looking over everything multiple times, preferably on multiple days. Assuming your spouse is not stateside, it's probably good to start being careful earlier in the process as the stakes may be higher with later stages of the process.
 
Certain filing errors will lead to a rejection without your application being considered further (as opposed to denial):
using the wrong version of a form missing biographic data for the petitioner or beneficiary missing a required signature (see USCIS Manual Volume 1 Chapter 2) not dating your signature lacking a handwritten (ink) signature (e.g. wrongly using an e-signature) At each phase, make sure you read over the instructions very carefully. Personally, I highlight with one color those instructions that don't apply to our case and another color those instructions that do. Then I can focus my attention on the ~20% of the instructions that apply to my case. I then make out a draft form in pencil and then once the data is complete, I start a typewritten PDF in Acrobat. With my spouse, I look over every response on the form 3 times on 3 different days. We check the form versions. We check the signatures and dates. We then go through the document checklist. We look over the cover letter to make sure the documents are ordered according to the list in the cover letter. It may seem a bit overkill, but I personally sleep better this way.
 
It's worth pointing out this excerpt from the I-130 instructions that you will also see in instructions for almost every form.
So, for example, if an applicant had no children, and the response to the number of children was omitted, the application can be considered incomplete. Conditional instructions (e.g. "if X, answer Question Y" or "if any") may allow answers to be omitted.  In my draft form, I highlight required responses based on instructions, which helps for reviewing the form for omission errors later.
 
VisaJourney has examples of I-130s here, but bear in mind that the form versions in the example are outdated.
 

The I-290B fee is $800!!!  The cost of a new I-130 is less than $700.  There is no guarantee the I-290B would even be approved.  

then it makes sense to re-file then.
Please scratch what I said before

I'm the petitioner (us citizen) and my wife is the beneficiary (from Turkiye). 
I'll complete a timeline in my profile when I have more time. Thanks again for your time. What you're saying makes sense, I think I'm just coming to grips with having to start from scratch.