Hello, 

I hope someone could help me  with this

Let say that I have a signal centered at 30Mhz with a BW of 1Mhz, and I try to take  it to zero-IF but because my local oscillator is not perfect the signal is finally taken a center frequency 300KHz. So  i got a side with negative frequencies from 300KHz to 0Hz.

 How these negative frequencies of its spectrum change the signal?

Is it possible to recover the signal by using a ADC?

thanks in advanced 

Your baseband signal should have a bandwidth of 500kHz, so 300kHz error sound very serious no matter what you want to accomplish at baseband. 300kHz error in a 30MHz carrier sounds excessive, by the way. No matter, my advice is fix the problem where it occurs at the L.O. You need to research carrier recovery and apply that to the L.O.

Is it possible to fix by digitising and signal processing - yes. You could digitise and mix with a quadrature NCO ay the error frequency and recentre the spectrum. The NCO would have to track the LO drift and for sure this isn't fixed at 300kHz, so you are back to fixing the L.O drift, but in a less direct way. 

Thank you, i'll follow your suggestions

I'm going to try to understand what you "meant", and comment based on those assumptions.

First, in my mind, zero-IF implies that correct downshifting would give you a signal spanning +- 500kHz from the 1 MHz BW you suggest.

If you do the down-shift with a real only system, then the resulting baseband spectrum will be symmetric around DC, and the content in the upper half of the source spectrum will overlap (reversed) the bottom half of the spectrum from the passband signal.
If you do the downshift with a complex system, then you will have a quadrature spectral result, and all that is lost is the details at DC from the very center of the original signal.  (Which probably has no content, because of the baseband generation that created the passband signal in the first place)
Now, if you actually end up with 300 kHz IF instead of 0, then you will have negative frequency content from -200 kHz to DC and then 800 kHz of content above DC.

Again, if your shift is real only, you will have spectral folding in the -200 kHz to 0 kHz combined with content from 300 kHz to 500 kHz, and you spectrum will be +- 800 kHz symmetric.
If you shift with a quadrature system, then you have a total of 1 MHz BW with data lost from the region around the new DC which would damage data that is 200 kHz from the bottom edge of the passband signal, and some junk at what should have been DC and is now + 300 kHz.

Now to your real question.  If you have a quadrature sampling A/D system with proper IQ inputs, then you can recover most of what you desired in spite of the 300 kHz offset, so long as the A/Ds are sampling above 800 kHz.  The only damage will be in the region around 200 kHz from the bottom of the original 1 MHz spectral bandwidth.
Also, in the baseband, you can correct the 300 kHz offset with some carrier recovery techniques as suggested by jfrsystems.

If you only have a real channel for the A/D, I'm sorry to say, that you loose, and the damage (over 600 kHz of the 1 MHz content) is not correctable to the best of my knowledge.

There's a big difference in the answer depending on what kind of downconversion you used to mix it from 30MHz to the 300kHz remaining offset.   If you used a complex-valued quadrature conversion, you will have a complex-valued signal, with I and Q components, still with 1MHz bandwidth just centered at 300kHz instead of 30MHz.  You can convert that to digital with two ADCs with no loss of signal bandwidth or significant distortion.

If you downconverted it from 30MHz to 300kHz with a real-valued sinusoid, then there will be two, overlapping, spectra centered at 300kHz and -300kHz, and the overlap will likely cause severe distortion of the signal.  You can digitize the distorted signal with a single ADC, but it is already distorted.

You don't really say, but if you intended to mix it so that it the 1MHz BW was centered at 0 Hz, i.e., it occupies -500 kHz to +500kHz, if you did that with a real-valued LO the signal would already be distorted by it and it's mirror image overlapping.  You can still digitize it with a single ADC, but it'll be a mess already.