I worked for a part of the year outside the Netherlands (for a Dutch company). Do I get a tax refund? And if yes, will this affect my continuous residence and my application for citizenship?
Important to know is whether the income which you earned outside the Netherlands is taxable in the Netherlands. I assume you have kept your main residence in the Netherlands while working outside the Netherlands.
In general income from employment is taxed in the country where the actual work is done. This is different in case the applicable tax treaty includes the so called 183 days ruling which states that if you have worked in the other country for less than 183 days in that (calendar) year for an employer who doesn‘t have a presence in that country or is linked with a company which covers the costs of your foreign employment. In that case the income will remain taxable in the Netherlands. Otherwise you may receive a refund, especially if your employer has withheld wage tax for the whole year, in which case you will have to declare the related income in the country in which you worked. Be aware that this may have consequences for any deductions you may be entitled to.
Also look at the premiums social security which have to be paid in the country where the work is done unless the national security organisation in the Netherlands has issued an A1 statement stating that you are covered in the Netherlands the entire year.
The longer the foreign period of employment the more relevant the tax and premiums consequences will be.
If you remained employed by the Dutch company (on a Dutch payroll) and had your main residence in the Netherlands I don‘t expect problems with your residence permit. But this may have to be investigated more thoroughly too.