Anyway, I found it by using zip4j. Fwollowing snippets can be used for creating both password protected and non-password protected files.
For the files to be password protected:
ZipFile zipFile = new ZipFile(zipFileName);
ZipParameters zipParameters = new ZipParameters();
zipParameters.setCompressionMethod(Zip4jConstants.COMP_DEFLATE);
zipParameters.setCompressionLevel(Zip4jConstants.DEFLATE_LEVEL_NORMAL);
zipParameters.setEncryptFiles(true);
zipParameters.setEncryptionMethod(Zip4jConstants.ENC_METHOD_AES);
zipParameters.setAesKeyStrength(Zip4jConstants.AES_STRENGTH_256);
zipParameters.setPassword(password);
zipFile.addFiles(new ArrayList<>(filesToZip), zipParameters);
And the files that are not password protected:
ZipFile zipFile = new ZipFile(zipFileName);
ZipParameters zipParameters = new ZipParameters();
zipParameters.setCompressionMethod(Zip4jConstants.COMP_DEFLATE);
zipParameters.setCompressionLevel(Zip4jConstants.DEFLATE_LEVEL_NORMAL);
zipFile.addFiles(new ArrayList<>(filesToZip), zipParameters);