Into the security business despite a criminal record?
You are allowed to take the expert knowledge examination according to § 34a Gewo in any case. The IHK does not check previous convictions. This is not the task of the IHK, but the examination of the required qualification. In case of doubt, however, you will not be allowed to work because you lack the necessary reliability. This is checked by the competent authority when the (potential) employer applies via the guard register. The residence authority also obtains information from other offices, for example from the Federal Central Register or the Federal Office for the Protection of the Constitution.
Regarding previous convictions:
If you receive a fine of 90 daily rates or more, you are considered to have a criminal record. It may also depend on the type of previous conviction and how long ago it was committed. Offences committed under juvenile criminal law are usually no longer relevant later on. If you have been convicted of a crime, this may clearly prevent you from working, depending on the type of offence.
The competent authority makes the final decision. The decision is not only based on data from the (extended) certificate of good conduct, but also on information about possible ongoing investigations and findings from police authorities, from the Office for the Protection of the Constitution or information available from your residence authority. This comprehensive check is carried out as part of the notification to the guard register, which the security company is obliged to make.
I would recommend you to proactively talk to the responsible local authority in advance.
There are numerous examples in the past where even relevant previous convictions did not prevent a person from working as a security guard. In case of doubt, however, this is an individual decision by the authority, which has its own discretionary powers to a certain extent.