There may be a solution via jquery code but as I'm not a developer last time I needed such functionality I helped me with the following approach:
Now the magic is to combine those fragments to the full date and safe it to your column.
You can do so by having a formula field on your form that combines everything to a date and is connected to your column or read those fragments within a workflow and save it.
Would that be helpful?
with jQuery you could do it eg. following way.
configure a class for datetime control, eg. OnlyHalfHour
NWF$('.OnlyHalfHour select.nf-datepicker-select:not(.nf-hours) :not(option[value="00"], option[value="30"])').remove();
I'm not sure ....
have you retyped the code exactly as provided above (with all spaces, comas, etc.)?
have you configured a class for date control?
were you applying the script on minute's or hour's dropdown?
any errors on developer console?
what platform and version are you on?