In general it is not supported, only what you can do is catch setExtrems() event (zoom) and load new data with new steps.
http://api.highcharts.com/highstock#xAxis.events.setExtremes http://api.highcharts.com/highstock#Series.setData
Question
How can this be possible? All the values are integers and that vertical tick is set as increments of 1.
When I zoom into such halfstep period, the halfstep is not happening.
Solution
In general it is not supported, only what you can do is catch setExtrems() event (zoom) and load new data with new steps.
http://api.highcharts.com/highstock#xAxis.events.setExtremes http://api.highcharts.com/highstock#Series.setData