How can you check if a field exists in a section, not by entry?
The solution is to getEntryTypes() from your section and then access the getFieldLayout() to get to the getFields() (thanks again @Khalwat!). Example:

{% for section in sections %}
    {% if section.getEntryTypes()[0].getFieldLayout().getFields()[0].getField().handle == 'specificfield' %}
        do something
    {% endif %}
{% endfor %}


Notice though that I specifically search for the first occurances, in (most) other cases you should foreach the getEntryTypes() and getFields()