Selection/Extraction of features based on location AND attribute

Question

My data consists of a point layer (iceberg positions containing their acquisition date as attributes) and a polygon layer (areal extends of DEMs also containing the acquisition date).
My aim is to select/extract the features based on their same location (the iceberg positions overlapping with the DEM extends) AND under the condition that they possess the same acquisition date.
Unfortunately I couldn't figure out how I can solve this problem.
What I tried is:

Extracting by location, which only fulfills the condition that their locations overlap
To figure out how to run an extraction/selection based on the attributes of different layers, which I haven't figured out yet

JGH · Answer

You can use a virtual layer to join the layers. You can then save as the output if you want to persist the data.
Go to the menu Layer > Add Layer > Add/Edit Virtual Layer... and enter the following query. Replace the layer name for yours
select pt.*, poly.ID
from mypointlayer pt
join mypolygonlayer poly
 on st_intersects(pt.geometry, poly.geometry)
    AND pt.acquisition_date = poly.acquisition_date

Val P · Answer

You can achieve your request using the tool Select feature by expression available in the selection Toolbar. 
Here, having the point layer active in the TOC, you can use this expression
contains(
aggregate(
layer:='polygon',
aggregate:='collect',
expression:=$geometry,
filter:="date" = '2020-09-06'
)
,$geometry)

This will select all the points that are inside the polygons that respect the filter rule: in this case only the polygons that have a specific data as attribute.

Having all the requested point selected you can now create a new layer exporting only the selected features.

Selection/Extraction of features based on location AND attribute

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