follow convention of cron, schedule with name=value pairs at the end of each line.

Everything up till the % character is just like the normal Jenkins Cron-like scheduler. Then after the % character you should format your parameters as name value pairs separated by equals and semicolons: name=value;othername=othervalue

There are of course limitations to what can be passed as parameters. As well as what types of parameters can be assigned. The internal mechanism leans on the same HTTP POST request method for triggering builds as documented in Launching a build with parameters.

This is a first step toward solving this Jenkins issue.

Examples:

# every fifteen minutes (perhaps at :07, :22, :37, :52)
H/15 * * * * %name=value

# every ten minutes in the first half of every hour (three times, perhaps at :04, :14, :24)
H(0-29)/10 * * * * % name=value; othername=othervalue
# every fifteen minutes with timezone
TZ=Australia/Sydney
H/15 * * * * %name=value
# every fifteen minutes with percent sign in param key/value
H/15 * * * * %name=value;key=10%;