Originally Posted by EMAW

There is some muddy water here but the simple answer is only log PIC time for those flights in which you are listed as PIC on the paperwork.
One other note. ALL 135 passenger ops require an SIC UNLESS the operator holds OPSPEC A015 (use of auto pilot in lieu of SIC) which applies to aircraft with 9 passengers or less.

Yes the 300 is Type Certificated for Single pilot, so provided you complete all the other training and do not have the “SIC REQUIRED” limitation on your certificate you can operate single pilot as long as the operation allows it.