Both spellings are correct. Speakers of US English only use the 'ize' version. British/Commonwealth English speakers use both 'ise' and 'ize'. The same goes for many verbs, such as realise/realize, recognise/recognize, and many others. It doesn't matter which convention you use, providing you are consistent.

Modernize is the American version, modernise is British spelling. There are many words like this (criticize vs criticise, realize vs realise...) When you're not sure, you can check here: https://dictionary.cambridge.org/dictionary/english/modernize