Rules of discovery are supposed to control the disclosure of evidence. But if the evidence is truly unknown until mid trial, the judge may have the discretion to admit it. Your lawyer can object, and ask for a continuance, or seek a mistrial, but ultimately it is his judgement as to what strategy to take, and it is up to a judge to decide how to handle this.
The response I have provided is general in nature, and does not create an attorney-client relationship. My practice is based in Rhode Island, and the law and practice in other states or jurisdictions may be different.
Each state has different rules regarding discovery and what must be shown to the defense prior to trial. If the prosecutor had to disclose the evidence prior to trial and failed to do so, then he or she should not be allowed to present it. However, if the evidence was not of the kind which must be disclosed then he or she would be free to present it.
Please remember that if you find an answer particularly helpful, please mark it as helpful or "best answer" so that the attorneys who volunteer their time to answer these questions have feedback. This answer is only for informational purposes, is not legal advice, and does not create an attorney-client relationship. Every case is different and must be judged on its own unique facts.
Generally speaking, there must be full disclosure, especially of any evidence that might be "exculpatory"...but I would need to know more about the details before I could give a definite answer. And, by the way, you should be discussing this in detail with your lawyer!
Discovery is ongoing in a criminal proceeding. Generally, the prosecution is obligated to disclose evidence upon discovery of that evidence. So, the answer to your question depends on when the evidence was discovered, what type of evidence it was, and when disclosure of it should have been reasonably made.