Is there any known medicine that can cause asthma in a child as a side effect?

Yes, beta blockers. Beta agents relax airways and are used to treat asthma. Beta blockers are a group of drugs used primarily by heart and thyroid doctors that block this relaxing of the airways and can cause wheezing; the effect is not permanent and the wheezing will resolve if the beta blocker is stopped.
No. Asthma is an inflammatory condition of the lungs, almost always caused by allergy in children. Medications don't cause inflammation as a side effect. An allergy to a medication can induce sudden and severe wheezing, but this is generally obviously related to the drug, which is then stopped. Continued use of the medication won't cause asthma without other evidence of a drug allergy.