Yes, you can be delusional about something that you firmly believe to be real but that, in actuality, does not exist. This type of delusion is known as a "bizarre delusion" or a "delusion of imagination."
Delusions are false beliefs that persist despite evidence to the contrary. They are often associated with psychiatric conditions, particularly psychotic disorders such as schizophrenia, schizoaffective disorder, or delusional disorder. Delusions can be diverse in content and can involve various themes, such as persecution, grandiosity, jealousy, or somatic concerns.
A non-bizarre delusion is one that is plausible, though still false. For example, a person might believe that they are being followed or monitored by the government, which is an idea that could potentially happen, but there is no actual evidence to support it. This type of delusion is non-bizarre because it is within the realm of possibility, even though it is not true.
On the other hand, a bizarre delusion is one that is implausible and clearly contradicts reality. For example, someone might believe they have superpowers, can communicate telepathically with aliens, or that they are a historical figure reincarnated. These beliefs are bizarre because they go beyond what is possible or realistic.
So, yes, it is possible for a person to have a delusion about something they firmly believe to be real, even though it does not exist or is not possible in the real world. These delusions can significantly impact a person's thinking, emotions, and behavior and may require psychiatric evaluation and treatment.