Anything related to OSHA or HVAC can't hurt. I also encouraged my maintenance and groundskeeper to take some kind of environmental class, learning how to be more green, whether it's having efficient windows, furnaces, etc. Looking for classes for them now into 2019.
I learned that certifications may help, but they are not the determining factor in getting promoted. Learning about financials and the management side of business would definitely help, along with great work ethic and the willingness to take on more responsibilities.
A few suggestions for technical credentials that I've found helpful.
Certificate for Apartment Maintenance Technician (CAMT)
Certificate for Apartment Maintenance Technician plus Energy Efficiency (CAMT+E)
Certificate For Apartment Maintenance Technician plus Leadership (CAMT+L) <Expected in June>
Certified Pool Operator
OSHA 10 hour or 30 hour
local Electrical credential (if offered/or required)
EPA section 608
HVACR R410A
HVAC Excellence Work Ready Certification (various topics)
HVAC EXcellence Professional Level Certification (various topics)
If I could make a suggestion, take a financial awareness course and learn about budgeting and the money end of the business. It may also be useful to expand awareness of leasing and marketing to see how maintenance activities can affect these areas.